Ana Torre Carrillo Facultad de Ingeniería Civil, Universidad Nacional de Ingeniería Av. Túpac Amaru 210, Lima 25 (Peru)

Transcription

1 Alcaton of te Monte Carlo metod to estmate te ncertant n te comressve strengt test of g-strengt concrete modelled wt a mltlaer ercetron Estmacón de la ncertdmbre de n ercetrón mltcaa ara la modelzacón del ensao de resstenca a comresón del concreto de alta resstenca medante la alcacón del método de Monte Carlo Isabel Morom Nakata Man and corresondng ator Facltad de Ingenería Cvl, Unversdad Naconal de Ingenería Av. Túac Amar 0, Lma 5 Per morom@n.ed.e Francsco García Fernández Escela Técnca Seror de Ingenería de Montes, Forestal del Medo Natral Unversdad Poltécnca de Madrd Cdad Unverstara s/n, 8040 Madrd San francsco.garca@m.es Ana Torre Carrllo Facltad de Ingenería Cvl, Unversdad Naconal de Ingenería Av. Túac Amar 0, Lma 5 Per anatorre@n.ed.e Pedro Esnoza Haro Facltad de Ingenería Indstral de Sstemas, Unversdad Naconal de Ingenería Av. Túac Amar 0, Lma 5 Per ces67@gmal.com Ls Acña Pnad Facltad de Ingenería Indstral de Sstemas, Unversdad Naconal de Ingenería Av. Túac Amar 0, Lma 5 Per lacna@n.ed.e Manscrt Code: 067 Date of Accetance/Receton: / DOI: /RDLC Abstract Te se of artfcal neral networks as a modelng tool for te sc-mecancal roertes of dverse materals as eerenced great advances n te last ten ears, manl de to te ncreased n comtng caactes of comters. Ts tecnqe as been sed n man dfferent felds of scence and ts effectveness s sffcentl roven. Its alcaton n te artcle board ndstr comles wt te reqrements of te test reglatons for te se n rodcton control, as an alternatve metod to normalzed one. However, n ste of rovdng a reslt wt a great aromaton, te do not ndcate antng abot te ncertant of te reslt. Ts last ont s crcal wen te reslts ave to be comared wt a rodct standard. Tere are nternatonall acceted determnstc tecnqes for obtanng te ncertant of a test reslt, alwas startng from te knowledge of te fncton tat relates te measre wt te measrement arameters. However, tese tecnqes are not entrel adeqate for te case of ecessvel comle fnctons sc as an artfcal neral network. In tese cases, te se of stocastc smlaton metods sc as te Monte Carlo metod s more arorate. In ts artcle, an artfcal neral network wll be develoed to obtan te comressve strengt of g-strengt concrete to later obtan te ncertant b a Monte Carlo smlaton. Ke words: Artfcal neral network, comressve strengt, g-strengt concrete, ncertant, Monte Carlo, GUM. Resmen La tlzacón de las redes neronales artfcales como erramenta de modelzacón de las roedades físco-mecáncas de m dversos materales a eermentado n gran avance en los últmos dez años debdo rncalmente al ncremento de las caacdades de cálclo de los ordenadores. Esta técnca a sdo emleada en m dversos ámbtos de la cenca s efectvdad está sfcentemente acredtada. S alcacón en la ndstra de tableros de artíclas cmle con los reqstos de las normatvas de ensao ara la tlzacón en el control de rodccón de métodos alternatvos al normalzado. Sn embargo, ese a roorconar n resltado con na gran aromacón, no ndcan nada sobre la ncertdmbre de dco resltado. 39

2 Y este últmo nto es crcal cando se comara el resltado con la esecfcacón del rodcto. Esten técncas determnstas, acetadas nternaconalmente, ara la obtencón de la ncertdmbre de n ensao, semre artendo del conocmento de la fncón qe relacona el mensrando con los arámetros de medda. Sn embargo estas técncas no son del todo adecadas ara el caso de fncones ecesvamente comlejas como es el caso de na red neronal artfcal. En estos casos es más adecado la tlzacón de métodos estocástcos de smlacón como el método de Montecarlo. En este artíclo se va a desarrollar na red neronal artfcal ara la obtencón de la resstenca a comresón del concreto ara osterormente obtener la ncertdmbre medante na smlacón de Montecarlo. Palabras clave: Red neronal artfcal, resstenca a comresón, concreto de alta resstenca, ncertdmbre, Montecarlo, GUM. Introdcton In recent ears, te develoment of ncreasngl owerfl comters as contrbted to an ncrease n te se of modelng tecnqes sng artfcal neral networks n dfferent areas of researc. Varos alcatons from ome rces valaton Nñez Tabares, Re Carmona & Cardad Ocerín, 03 to engneerng Çanakc, 007 ave benefted from tese owerfl modelng tools. Tese tools rovde a sbstantal mrovement over an revosl roosed model, regardless of ts natre, wt te added advantage tat te do not need an ror assmton abot te statstcal strctre of data Kosrav, Naavand, Cregton & Ata, 0a. Major advances ave been made n ndstral rocess control, manl becase te are caable of modelng comle relatons and can adeqatel redct weter or not te rodct caracterstcs are n lne wt secfcatons Sktoma & Tannock, 005. Te ave been wdel sed to caracterze dfferent materals sc as cement Bakasoğ, Del & Tanış, 004, concrete Blm, Atş, Tanldz & Karaan, 009; Sandemr, 009; Özcan, Atş, Karaan, Uncoğl & Tanldz, 009 and certan metals Mkerjee, Scmader & Rüle, 995; Malnov, Sa & McKeown, 00; Hassan, Alrasdan, Haajne & Maas, 009; Ozerdem & Kolksa, 009. Neverteless, a neral network tself does not rovde an nformaton on confdence ntervals or reslts ncertant Kosrav et al., 0a. Ts ncertant s mortant not onl as ndcatve of measrement rocess qalt, bt also rovdes a confdence nterval on reslts Solagren-Beascoa Fernández, Alegre Calderón & Bravo Díez, 009. Accordng to te nternatonal acceted defnton, te ncertant assocated wt a measrement can be defned as te sqare root of te varance of ts robablt denst fncton. In ts contet, te Gde to te Eresson of Uncertant n Measrement GUM BIMP, IEC, IFCC, ISO, IUPAC & OILM, 995 ndcates a metod to obtan te ncertant on a measrement from te nt arameters vales and ter robablt dstrbtons. In most cases, te measrand s derved from a drect measrement, t s not dffclt to assess ts ncertant. However, sometmes te measrand s defned as a fncton of te nt vales. In tese cases, te ncertant on te measrand can be obtaned b te law of roagaton of te varances BIMP et. al, 995.Te se of ts metodolog mles a knowledge of te fncton relatng te nt arameters wt te measrand. Ts s dffclt wen te model s derved trog te nmercal solton, for eamle, n case of models defned b dfferental eqatons Esward, Gnestos, Harrs & Hll, 007 or wen te model s ecessvel comle and nonlnear,.e. n te case of an artfcal neral network. In tese cases, as well n te case of domnant contrbton from a non-normal dstrbton fncton or wen te dstrbton fncton of te measrand s asmmetrc, an evalaton of te ott ncertant based on te law of roagaton of ncertant wll rovde vales not entrel relable Esward et al., 007. To solve tese roblems, te Workng Gro of te Jont Commtee for Gdes n Metrolog JCGM reared a slement to te GUM descrbng ow to obtan te ncertant on te measred trog smlaton b te Monte Carlo metod JGCM, 008. Ts metodolog s generall vald for a larger gro of statons tan te GUM Müller et al., 008. Ts artcle develos a new metodolog, based on te smlaton b te Monte Carlo metod as descrbed n Slement of te GUM JGCM, 008, to evalate te ott ncertant of a mltlaer ercetron sed to model te testng for comressve strengt of g-strengt concrete accordng to ASTM C 39 / C 39M ASTM, 00 wt dfferent crng tmes. Te mltlaer ercetron s a te of network wdel sed to std te mecancal roertes of dfferent constrcton materals, not onl cement Sarıdemr, 009; Özcan et al., 009, bt also basalt Çanakc, 007, varos metals Ozerdem & Kolksa, 009; Redd, Krsnaa, Hong & Lee, 009 or wood-based anels Cook & C, 997. In all cases, reslts ndcate ver good correlatons between actal vales and tose smlated b te neral network. However, none of tese stdes rovde an nformaton on te ncertant on te network ott vales. 30

3 Hg-strengt concrete Materals and Metods Ts std sed 054 secmens of g-strengt concrete made wt dfferent tes and amonts of cement, sand, coarse aggregate and water. Te secmens for comresson testng were made accordng to ASTM standard C 9 / C 9M ASTM, 000. Comresson tests were carred ot accordng to ASTM standard C39 / C 39M ASTM, 00 after dfferent crng tmes. Aal comresson tests were carred ot on a Ton Tecnk macne wt a 3000KN cell and a Tns Olsen macne wt a 500KN cell A. Followng te reslts of smlar stdes Torre, García, Morom, Esnoza & Acña, 05; Acña, Torre, Morom & García, 04, te elanator varables cosen to model te comressve strengt of concrete were: crng tme; te, amont and ercentage of addtve; te, amont and ercentage of mcroslca; amonts of water, coarse aggregate, sand and cement; te nomnal mamm coarse aggregate sze; secfc wegts of sand and coarse aggregate; and te water-cement rato. Te Table sows te nstrments sed for testng, as well as ter range of measrement and ncertant. Table. Instrments sed for varables measrements. Sorce: own elaboraton. Instrment Uncertant Seve3/4" Seve Scale 0-00 kg Scale g Verner0-300 mm 0.05 mm 0.04 mm 0.0 kg.5 g mm Mltlaer ercetron Te mltlaer ercetron Fgre cold be defned as a comtng sstem tat mtates te comtatonal caabltes of bologcal sstems b sng a large nmber of nterconnected elements. Its caracterstcs as a nversal aroac fncton Hornk, 989 allows te modelng of comle nonlnear relatonss. Fgre. Feed-forward mltlaer ercetron neral network. Sorce: own elaboraton. To desgn a mltlaer ercetron s a slow and comle rocess. Tere are no fed rles to establs te nternal strctre of te network. However, tere are a nmber of recommendatons avalable regardng ts desgn, based on te qantt of avalable data Sa, 007, or on te most desrable te of confgraton Vanstone & Fnne, 009. Tere are as well a nmber of condtons tat mst be met to ensre tat te network wll erform roerl, esecall concernng te avodance of overfttng Bso, 995. To avod overfttng and to evalate te relablt of te network, te ntal dataset was randoml dvded nto tree sbsets: te tranng, valdaton and testng sbsets. Te frst two were sed for te tranng ase and for te reventon of overfttng, resectvel. Te trd sbset was sed to assess te level of relablt of te network Bso, 995. Te sgmod erbolc tangent Eq. was sed as a transfer fncton; t s matematcall eqvalent to te erbolc tangent, bt mroves te network erformance Demt, Beale & Hagan, 00. 3

4 3 e f f: neron ott vale. : neron nt vale. Te vales of all varables, bot deendent and ndeendent, were normalzed to avod large vales of, for wc te dervatve of f s close to zero. Ts ermts a ger effectveness of te transfer fncton Eq. Demt, Beale & Hagan, 00. mn ma mn X X X X X X :vale after normalzaton of vector X. Xmn Xma: mamm and mnmm vales of vector X. Te tranng algortm sed was te reslent backroagaton, wc greatl mroves te reslts wt sgmodal transfer fnctons Demt, Beale & Hagan, 00. Modelng wt artfcal neral networks can rovde ott vales wc closel aromate to te eermental vales obtaned n laborator, bt t cannot rovde an estmaton of te ncertant assocated wt te ott vale. Ts ncertant s te reslt, on one and, of te smlfcaton of te enomenon b modelng matematcall; and on te oter and, of te varablt and nose wc are nerent n te nt vales Mazlom, Rose, Crre & Mordor, 0. Varos stdes ave been ndertaken to obtan confdence ntervals, bt alwas n artclar cases, sc as ercetrons wt onl one dden laer, wt normal dstrbtons of te nt varables, or wt te assmton of normalt of te ott errors Kosrav et, al, 0a; Paadoolos, Edwards & Mrra, 00; Crssolors, 996. Tese artclar cases do not cover te wole feld of develoment of neral networks snce te do not consder cases for wc te ercetron as more dden laers Fgre or anoter te of network. Calclaton of test ncertant Te GUM BIMP et al., 995 ncldes a seres of nternatonal recognzed recommendatons to evalate te ncertant on measrement reslts. It ntrodces n artclar te law of roagaton of ncertant to obtan te ncertant on a measrement from te ncertantes of varables nvolved n te rocess: If = f,,...n s te fncton tat determnes te fnal vale of te measrement reslt and =,..., are all varables tat nflence te measrement reslt, te law of roagaton of ncertant secfes tat te combned ncertant of te fnal vale of te reslt s defned b Eq. 3:,...,..., j j j j j 3 : combned test ncertant : varables nflencng te measrement : measrement ncertant of varable.

5 =f: fncton relatng te measrements wt te measrand γ, j: correlaton coeffcents between varables. Correlaton coeffcents between te dfferent varables nvolved n te rocess, γ, j, reresent te ossble nflence tat ma ave one measrement wt one nstrment, over anoter measrement erformed later wt te same nstrment or a dfferent one. Te adatve Monte Carlo metod Te GUM BIMP et al., 995 attemts to cover a varet of dfferent statons tat can occr drng te measrement rocess. However, n man cases, sc as te non-normalt of a ke nt varable, or te comlet of te fncton relatng nt and ott varables, or te lack of normalt of te ott errors, sng te law of roagaton of ncertant can rovde nrelable reslts Esward et al., 007. Te Slement to te GUM JGCM, 008 descrbes a nmercal metod based on Monte Carlo smlaton to calclate ts ncertant. Te nmber of smlatons wll deend on te degree of confdence desred for te reslts. As general rle, 0 6 smlatons are sall reqred to obtan 95% confdence ntervals JGCM, 008. However several factors, sc as te natre and te of dstrbton of te nt data, te model fncton, or te natre tself of ott vales Y, can nflence te reqred nmber of smlatons. Te adatve Monte Carlo metod descrbed n secton 7.9 of Slement JGCM, 008 solves ts roblem b determnng te nmber of smlatons trog an teratve metod based on te desred level of recson for te ncertant and te reqred confdence nterval: Let δ be te accetance factor, fncton of te reqred accrac Eq. 4: 0 n 4 n: reqred nmber of sgnfcant dgts. δ: nmercal tolerance factor. Let M be te nmber of data for eac smlaton, fncton of te reqred coverage factor Eq. 5: M Ma 0 4, J 5 J: rondng down of 00/-q. q: coverage robablt reqred. M: nmber of Monte Carlo trals.. Let te arameter = be te nmber of tmes to reeat te rocess tll te nmercal tolerance factor s reaced.. Randoml te set X,. m of M data s generated, to obtan a matr of dmenson M, were s te dmenson of te nt vector nmber of nt varables and M te arameter s calclated above. A 3. Te smlaton seqence of te model s carred ot for te M data Eq. 6. Y f X f 6 Y: ott vector. X: nt vector. f: model fncton. 4. Startng from = M, comte for eac smlaton seqence : a. Mean Eq

6 M M 7 M: nmber of Monte Carlo trals. : mean of eac smlaton. b. Uncertant, comted lke te standard devaton Eq. 8. M 8 M M: nmber of Monte Carlo trals. : mean of eac smlaton. : ncertant assocated wt eac. 5. If =, ncrease t b and retrn to ste After eac smlaton seqence, calclate: a. Mean and standard devaton of Eq. 9. s ˆ ˆ ˆ 9 : nmber of smlaton trals. : mean of eac smlaton tral. ŷ: mean of all te smlaton trals. Sŷ: standard devaton of te smlaton trals. b. Mean and standard devaton of Eq. 0. s ˆ ˆ ˆ 0 : nmber of smlaton trals. : mean of eac smlaton tral. : ncertant assocated wt eac smlaton. û: meanof te ncertantes assocated wteacsmlaton. sû: standard devaton of te ncertantes assocated wt eac smlaton. 7. If an of te vales of Sŷ or Sŷ s larger tan δ, ncrease b and retrn to ste 4. Te followng gra Fgre descrbes te entre rocess for estmatng te ncertant of te ott data n a mltlaer ercetron. Fgre. Flowcart for te adatve Monte Carlo metod. Sorce: own elaboraton 34

7 Te evalaton of te confdence ntervals qalt s done wt te redcton ntervals coverage robablt PICP Kosrav et. al, 0a; Kosrav et al. 0a; Mazlom et al., 0 Eq. wc measres te nmber of eermental data nclded wtn te confdence nterval. Ts measre s a good ndcator of te qalt of te obtaned confdence ntervals Kosrav et al., 0b. PICP % c 0 00 n test n test t [ L, U ] t L, U c ntest: nmber of eermental data. L U: lower and er lmts of te confdence ntervals of te -t vale. t:-teermental vale. Accordng to Mazlom et al., 0 and Kosrav et al., 00, te PICP s eected to eceed 95%. All calclatons were done wt a secfc comter rogram develoed n MATLAB. Uncertantes on te nt varables Reslts Uncertantes on te nt and ott varables were obtaned from te test data calclated accordng to te roagaton of ncertant Teorem Eq. 3. Te vales obtaned for eac one of te nt arameters and ter ncertantes are sown n te followng Tables and 3. Tose ncertantes are obtaned from te calbraton certfcates of te nstrments Table combned wt te eterogenet ncertant from te varablt of varables. Table. Int varables for te neral networl model. Sorce: own elaboraton. Varable Mean Standard devaton Mnmm Mamm Uncertant Crng tme das Addtve % Addtve kg/m Mcroslca % Mcroslca kg/m Water / cement rato A Cement kg/m Nomnal mamm Aggregate sze Sand kg/m Table 3. Int constants for te neral networl model. Sorce: own elaboraton. Parameter Vale Uncertant Water L/m

8 Secfc wegt of sand Ton/m Coarse aggregate kg/m Secfc wegt of coarse aggregate Ton/m Artfcal neral network Te otmal arctectre for a mltlaer ercetron conssts of an nt laer of 5 varables, two dden laers wt 6 and neron eac and an ott of one varable. Te reslts of te tranng, valdaton and testng rocesses can be seen n te Table 4. Table 4. Reslt of te artfcal neral network desgn. Sorce: own elaboraton. Pase Strctre R R Error % Tranng Valdaton [5 6 ] Testng R and R are de correlaton coeffcents between eermental data targets and smlated data b te neral network otts. Fgre 3 sows te correlatons between te eermental data and te network reslts for te testng ase. Fgre 3. Correlaton between observed and redcted vales for te testng set. Sorce: own elaboraton. Te coeffcent of determnaton of te testng set Table 4 s 0.80, ndcatng tat te model s able to elan 80% of te samles varablt. Te Table 5 reflects te std of te dfferences between te eermental vales and tose obtaned b te network for te testng set. 36

9 Table 5. ANOVA table comarng eermental reslts wt tose obtaned b te artfcal neral network for te testng set. Sorce: own elaboraton. Sorce SS d.f. MS F P-vale Colmns Error Total SS: sms of sqares, d.f.: degrees of freedom, MS: mean sqares SS/d.f., F: Fser statstc, P-vale: -vale for F. Snce -vale s greater tan 0.05, tere are no sgnfcant dfferences between te eermental vales and tose obtaned b te artfcal neral network, at 95% sgnfcance level. Smlaton of te ncertant trog Monte Carlo smlaton Uncertant reslts obtaned trog te Monte Carlo smlaton on te tranng, valdaton and testng data sets are sown n te Table 6. Table 6. PICP for all te data sets. Sorce: own elaboraton. Set PICP % Tranng 98.3 Valdaton 98. Testng 97.8 Dscsson Te reslts obtaned wt te neral network are wtn te range of vales obtaned n oter stdes of modelng concrete roertes. Te reslts obtaned wt correlaton coeffcents between 0.90 and 0.9 are consstent wt tose obtaned b oter ators Lee, 003; Oztas, Pala, Ozba, Kanka, Caglar & Batt, 006; Ukranczk & Ukranczk, 008; Ozerdem & Kolksa, 009; Prasad, Eskandar & Redd, 009; Yarak, Karac & Demr, 03, wo obtaned correlaton coeffcents between 0.8 and Smlarl, te determnaton coeffcents R = 0.80 and R = 0.8 are ger tan tose reorted b Ye 998 and smlar to tose b Oztran, Ktl & Oztran 008, wo obtaned mamm coeffcents of Te vales obtaned for PICP are abot 98% Table 6 ndcatng tat nearl all te eermental data are nclded wtn te confdence nterval. Tese vales for te PICP are above 95% level ndcated b Mazlom et al. 0 and are wtn ranges obtaned b Mazlom et al. 0, Kosrav et al. 0a or Kosrav et al. 0b, wo obtaned confdence ntervals between 75% and 00%, deendng on te metod sed for te smlaton. Or reslt obtaned s better tan te reslt reorted n a std of confdence ntervals for te forecasts n energ markets Kosrav et al., 00, were PICP between 9.6% and 94.% were obtaned. Te reslt s also seror to te one obtaned b Srvastava & Pangra 03 on a std of confdence ntervals for te demand redcton n te electrct market, wc obtaned a PICP between 50% and 00%. It s also ger tan reslts reorted b Wan et al. 04, wt 95% of coverage factor, obtaned a PICP between 89.6% and 99.6%, deendng on te modelng metod. And t s consstent wt te reslts of Kosrav & Naavand 04, wt obtaned PICP vales over 95% wt more tan 50 smlatons. Conclsons An artfcal neral network as been obtaned wt a confdence level sc tat cold be sed as an alternatve to te standard metod to redct reslts of comressve strengt of g-strengt concrete. Monte Carlo metod as been sed to obtan te ncertant on te ott vales of an artfcal neral network, resltng n confdence level smlar to tose of oter stdes. Terefore, tese reslts ave roven te valdt of sng te Monte Carlo metod to smlate te ncertant n comressve strengt vales obtaned wt an artfcal neral network. 37

10 Te ossblt of sng artfcal neral networks s oened for n-factor control of comressve strengt, snce te ncertant assocated wt te test ermts te evalaton of te degree of comlance / non-comlance wt a secfcaton wen te reslts are close to te secfcaton lmts. Acknowledgements Ts work was sorted b te Fondo ara la Innovacón, la Cenca la Tecnología FINCYT Project37-FINCYT-IA-03 Lma Perú, te ators acknowledges te General Researc Insttte of Natonal Unverst of Engneerng IGI-UNI for ts sort. References Acña L., Torre A., Morom I., García F. 04. Use of artfcal neral networks to redct te comressve strengt of concrete accordng to ASTM C39/C 39M standard. Informacón Tecnológca, 54, 3-. ASTM ASTM C 9/C 9M. Standard Practce for Makng and Crng Concrete Test Secmens n te Laborator, ASTM Internatonal, 00 Barr Harbor Drve, PO Bo C700, West Consoocken, PA , Unted Estates. ASTM 00. ASTM C 39/C 39M. Standard Test Metod for Comressve Strengt of Clndrcal Concrete Secmens, ASTM Internatonal, 00 Barr Harbor Drve, PO Bo C700, West Consoocken, PA , Unted Estates, 00. Bakasoğ A., Del T., Tanış S Predcton of cement strengt sng soft comtng tecnqes. Cement and Concrete Researc, 34, Blm C., Atş C.D., Tanldz H., Karaan, O Predctng te comressve strengt of grond granlated blast frnace slag concrete sng artfcal neral networks. Advances n Engneerng Software, 40, BIMP, IEC, IFCC, ISO, IUPAC, OILM Gde to te Eresson of Uncertant n Measrement. nd edton. Internatonal Organsaton for Standardsaton, Geneva, Swtzerland. Bso C.M Neral networks for attern recognton. Oford Unverst Press. Çanakc H., Pala M Tensle strengt of basalt from a neral network. Engneerng Geolog, 94, 0-8. Crssolors G., Lee M, Ramse A Confdence nterval redcton for neral network models. IEEE Transacton n Neral Networks, 7, 9-3. Cook D.F., C, C.C Predctng te nternal bond strengt of artcleboard, tlzng a radal bass fncton neral network. Engneerng Alcatons of Artfcal Intellgence, 0,7-77. Demt H., Beale M., Hagan M. 00. Neral Network Toolbo User s Gde, Verson 4. Te MatWorks Inc., Natck, USA. Esward T.J., Gnestos A., Harrs P.M., Hll I.D A Monte Carlo Metod for ncertant evalaton mlemented on a dstrbted comtng sstem. Metrologa, 44, Hassan A.M., Alrasdan A., Haajne M.T., Maas A.T Predcton of denst, orost and ardness n almnm-cooer-based comoste materals sng artfcal neral network. Jornal of Materals Processng Tecnolog, 09, Hornk K., Stnccombe M., Wte H Mltlaer feedforward networks are nversal aromators. Neral Networks,, JCGM - Jont Commttee for Gdes n Metrologn 008. Evalaton of measrement data. Slement to te Gde to te eresson of ncertant n measrement Proagaton of dstrbtons sng a Monte Carlo metod. Kosrav A., Naavand S., Cregton D., Ata A.F. 0a. Comreensve revew of neral network-based redcton ntervals and new advances. IEEE Transacton n Neral Networks, 9, Kosrav A., Naavand S., Cregton D., Ata A.F. 0b. Lower er bond estmaton metod for constrcton of neral networks-based redcton ntervals. IEEE Transacton n Neral Networks, 3, Kosrav A., Naavand S., Cregton D. 00. Constrcton of otmal redcton ntervals for load forecastng roblems. IEEE Transacton on Power Sstems, 53, Kosrav A., Naavand S. 04. An otmzed mean varance estmaton metod for ncertant qantfcaton of wnd ower forecasts. Internatonal Jornal of Electrc Power and Energ Sstems, 6, Lee S.C Predcton of concrete strengt sng artfcal neral networks. Engneerng Strctres, 5, Malnov S., Sa W., McKeown J.J. 00. Modellng te correlaton between rocessng arameters and roertes n ttanm allos sng artfcal neral networks. Comtatonal Materals Scence,,

11 Mazlom E., Rose G., Crre G., Mordor S. 0. Predcton ntervals to accont for ncertantes n neral network redctons: Metodolog and alcaton n bs travel tme redcton. Engneerng Alcatons of Artfcal Intellgence, 43, Müler M., Wolf M., Rösslen M MUSE: comtatonal asects of a GUM slement mlementaton. Metrologa, 45, Mkerjee A., Scmader S., Rüle M Artfcal neral networks for te redcton of mecancal beavor of metal matr comostes. Acta Metallrgca Materala, 43, Núñez Tabales, J.; Re Carmona, F.; Cardad Ocern, J.M. 03. Imlct Prces n rban Real Estate valaton. Revsta de la Constrccón, 8-8. Özcan F., Atş C.D., Karaan O., Uncoğl E., Tanldz H Comarson of an artfcal neral network and fzz logc models for redcton of long-term comressve strengt of slca fme concrete. Advances n Engneerng Software, 40, Ozerdem M.S., Kolksa S Artfcal neral network aroac to redct te mecancal roertes of C-Sn-Pb-Zn-N cast allos. Materals and Desgn, 30, Oztas A., Pala M., Ozba E., Kanka E., Caglar A., Batt M.A Predctng te comressve strengt and slm of g strengt concrete sng neral network. Constrcton and Bldng Materals, 0, Oztran M., Ktl B., Oztran T Comarson of concrete strengt redcton tecnqes wt artfcal neral network aroac. Bldng Researc Jornal, 56, Paadoolos G., Edwards P.J., Mrra A.F. 00. Confdence estmaton metods for neral networks: A ractcal comarson. IEEE Transactons on Neral Networks, 6, Prasad B.K.R., Eskandar H., Redd B.V.V Predcton of comressve strengt of SCC and HPC wt g volme fl as sng ANN. Constrcton and Bldng Materals, 3, 7-8. Redd N.S., Krsnaa J., Hong S.G., Lee J.S Modelng medm carbon steels b sng artfcal neral networks. Materals Scence and Engneerng, 508, Sardemr M Predcton of comressve strengt of concretes contanng metakaoln and slca fme wt neral networks. Advances n Engneerng Software, 40, Sa W Comment on te sses of statstcal modellng wt artclar reference to te se of artfcal neral networks. Aled Catalss. A- General, 34, Srvastava N.A., Pangra B.K. 03. Pont and redcton nterval estmaton for electrct markets wt macne learnng tecnqes and wavelet transforms. Nerocomtng, 8, Solagren-Beascoa Fernández M., Alegre Calderón J.A., Bravo Díez P.M Imlementaton n MATLAB of te adatatve Monte Carlo metod for te evalaton of measrement ncertantes. Accredtaton and Qalt Assrance, 4, Sktoma W., Tannock J Te tranng of neral networks to model manfactrng rocesses. Jornal of Intellgent Manfactrng, 6, Torre A., García F., Morom I., Esnoza P., Acña L. 05. Predcton of comresson strengt of g erformance concrete sng artfcal neral networks. Jornal of Pscs: Conference Seres, 58, -6. Ukranczk N., Ukranczk V A neral network metod for analsng concrete drablt. Magazne of Concrete Researc, 60, Vanstone B., Fnne G An emrcal metodolog for develong stockmarket Tradng Sstems sng artfcal neral Networks. Eert sstems wt Alcatons, 36: Wan C., X Z., Pnson P., Dong Z.Y., Wong K.P. 04. Otmal redcton of wnd ower generaton. IEEE Transactons on Power Sstems, 93, Yarak H., Karac A., Demr I. 03. Predcton of te effect of varng cre condtons and w/c rato on te comressve strengt of concrete sng artfcal neral networks. Neral Comtng and Alcatons,, Ye I.C Modelng of strengt of g-erformance concrete sng artfcal neral networks. Cement and Concrete Researc, 8,