Wastewater Biodegradation Process Identification; a Multi Layer Approach via Distributions

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1 Prodgs of h 7 WSEAS I Cofr o Cllulr & Molulr Bolog - Bohss & Bogrg Ahs Gr Augus 6-7 Wsr Bodgrdo Pross Idfo; Mul Lr Aroh Dsruos CONSANIN MARIN EMIL PERE DAN SELIŞEANU Drm of Auomo Urs of Cro Cro Sr A I Cuz No3 ROMANIA mr@uo h://uomouro Asr: - h r xds h rodurs of sr odgrdo ross (WBP dfo s h frs rsd h uhors [] [] hs rodurs llo dfo of ll ross rmrs oh ss h r m os or m r h dfo rolm s formuld s odo o sh h xs rlo of h ssm hs rlo s rrsd fuols usg hqus from dsruo hor sd o sg fuo from f dmsol fudml s As h WBP xrsss rol dds rmrs d som msurl rls h m d of hs rodurs s o us hrrhl mul lr sruur of dfo hh llos og srg of lr lgr ssms of quos h uko rmrs h offs of hs lgr ssms r fuols ddg o h u d ouu rls lud hrough som sg fuos from dsruo hor Aordg o h roosd rodur h frs lr ol som s quos r lud hroughou sg fuos o o s of lr quos som rmrs h rsuls of hs frs lr of dfo r ulzd for xrssg ohr rmrs lr quos h x lr hs ross s rd ul ll rmrs r dfd h m r ls r xrssd s f dgr m olomls hos rmrs r ludd h s of rmrs o dfd Alos for rmr dfo of s r odgrdo rosss r rsd B xmls h ol of h mhod s rld K-Words: - Idfo; Borosss Wsr odgrdo Dsruo hor; Fuols Iroduo As rsd [] rogrsss h md h r of ouous-m ssm dfo M dsussos mhods d rsuls o ouous-m dfo r rsd []; [] [] [9]; [] [5] [6] A ol roh for ouous-m ssm dfo s h sd o dsruo hor usg drms dsruos [] or rdom dsruos [3] Idfo of h o-lr ouous-m ssms s fr mor omld h rdol rodurs r sd o h Volrr fuol srs xrssd m dom [3] or frqu dom [6] h rmr dfo of drms olr ouousm ssms (NCS modlld oloml dffrl quo hs osdrd umrous uhors [5] [6] I [] s rsd mhod for dfo of olr ouous m ssms (NCS osdrg h h uko rmrs r rol rlos h msurd rls Usg hqus ulzd dsruo roh [7] [] [9] h msurl fuos d hr drs r rrsd fuols o fudml s of sg fuos Suh ssms r ommo oholog [] [7] [] h m d from [] s o us hrrhl mul lr sruur of dfo Frs som s quos r ulzd o o s of lr quos som rmrs h rsuls of hs frs sg of dfo r ulzd for xrssg ohr rmrs lr quos hs ross s rd ul ll rmrs r dfd h o d of hrrhl mul lr sruur dfo hs xdd o m r ssms [] Vrl rmrs r modlld f dgr m olomls hos uko offs r ludd h s of rmrs o dfd o rsform dffrl m r ssm of quos o lgr ssm of fuols h so-lld ghd dsruos r osdrd Wghd dsruos r ohg ls rhr h rodu m fuos d dsruos h r s orgzd s follos: h mhml

2 Prodgs of h 7 WSEAS I Cofr o Cllulr & Molulr Bolog - Bohss & Bogrg Ahs Gr Augus 6-7 modl of sr odgrdo ross s g So So 3 rss som ss rgrdg dsruo roh of dfo h hrrhl sruur of dfo d smo quos ks h s of So Som xrml rsuls r rsd So 5 d olusos So 6 Mhml modl of sr odgrdo ross W osdr omho ross - sr odgrdo h roduo of mh gs h ks l sd Couous Srrd k Boror hos rdud modl s rsd [] I s o hss ross I h frs hs h gluos from h sr s domosd f oll ds (s roo d hdrog d org ro udr o of h dog r I h sod hs h osd hdrog domoss h roo d CH3CHCOOH s H d ro doxd CO I h frs mhog hs h s rsformd o mh d CO d fll h sod mhog hs h mh gs CH s od from H d CO [] [7] h follog smlfd ro shm s osdrd φ S X + S φ S X + P hr: S rrss h gluos susr S h susr X s h dog r X h ols mhog r d P rrss h rodu h mh gs h ro rs r dod φ φ h orrsodg dml modl s X X S k S DS d φ X = D X d φ + ( S k k 3 S P k P Q hr h s or of h modl s ξ = [ X S X S P] = [ ξ ξ ξ3 ξ ξ 5] (3 hos omos r oros (g/l h ro rs r olr fuos of h s omos xrssd s φ = φ( ξ = [ φ( ξ φ( ξ] ( h or of fd rs d of rs of rmol of omos s dod F = [ D S Q ] (5 hr D s h dluo r slr hs rulr s S rrss h oro of h xrll flu susr gluos Q s h mh gs ouflo r h dml modl ( oml r dξ / d = K φ( ξ D ξ + F (6 I f hs modl dsrs h hor of r lss of ohologl rosss I rfrs s h grl dml s-s modl of hs lss of orosss [] I (6 K s h so-lld mrx of h ld offs k k k = k 3 k K (7 h ro rs for hs ross r g h Mood l S X φ( ξ = µ ( KM + S d h Hld k modl S X φ( ξ = µ (9 KM + S + S / K hr KM K M r Mhls-M oss; µ µ rrs sf groh rs offs d K s h ho os For sml shll do h l rmrs h or = [ ] ( hr = k; = k; 3 = k3; = k ( 5 = µ ; 6 = µ ( 7 = KM ; = KM ; 9 = K (3 Bus h dluo r D xrll modfd ll osdrd h hrd omo of h u or u = [ u u u 3] h ohr o omos of u r h oro S d h mh gs ouflo r Q so u = S; u = Q; u3 = D ; ( Usull Q dds o s rls Q = Ψ( ξ drmg fdk o h u u Wr xll omos h s quos ( or (6 h h o oos ks h form ξ = φ u3 ξ (5 ξ ξ φ = 5 (6 7 ξ = φ u3 ξ + u u3 (7 ξ3 = φ u3 ξ3 ( ξ3 ξ ' φ = 6 ' 9 = (9 + 9 ξ 9 ξ = φ 3 φ u3 ξ ( ξ = u ξ + φ u ( 5 3 5

3 Prodgs of h 7 WSEAS I Cofr o Cllulr & Molulr Bolog - Bohss & Bogrg Ahs Gr Augus Dsruo roh of dfo L us do Φ h fudml s from dsruo hor [5] of h rl fudml fuos ϕ : ϕ( ( h om suor hg ouous drs ls u o h ordr A dsruo s lr ouous ( h o oolog rl fuol o Φ F : Φ ϕ F( ϕ L q: q( (3 fuo hh dms Rm grl o om rl from Usg hs fuo uqu dsruo Fq : Φ ϕ Fq( ϕ uld h rlo F ( ϕ = q( ϕ( ϕ Φ q I dsruo hor h oo of dsruo k- ordr dr k = : [5] s ( k k ( k Fq ( ϕ = ( Fq( ϕ ϕ Φ ( ( ϕ F k ( ϕ = ( k q( ϕ k ( ( q L o osdr dml ouous m ssm h u us u: u u( u Ω d ouus : ( Γ hr Ω rrss h s of dmssl us d Γ s h s of ossl ouus I xrssd dffrl oror q /( u = Q( u = (5 hos xrsso dds o or of rmrs = [ ] h oror (5 hos lss drmd rrss fml of modls h g sruur os rmrs A sl s s h modl (5 xrssg lr rlo h rmrs q /( u = Q( u = = (6 = hr d rrs sum of h drs of som ko ossl olr fuos ψ ψ h rs o h u d ouu rls ( ( = [ ψ ( u ] = : = [ ψ ( u ] (7 = = Prmrs r g gr umrs h dfo rolm o odo (6 hs uqu soluo A dfo rolm ms o drm h rmr = g h ror formo o h modl sruur Q (5 d h osrd u-ouu r ( u = ( u Q suh h q ( = /( u No l us osdr ko h s of ouous m slr fuos (7 ( ( ( = [ ψ ( ( ( ] = [ ψ ( ] = : = = ( ( ( = [ ψ( ( (] = [ ψ(] = = ( u (9 u Bsd o hs fuos h rgulr dsruos F = : r grd rlos ( = = ( Φ F Fψ F : ϕ F ( ϕ (3 ψ ( ( ( ϕ [ ( ] ( ( [ ( ] ( ψ ϕ ψ ϕ = = F = d= h osu h ro or ( [ ( ( ( ] F ϕ = F ϕ F ϕ F ϕ (3 Also h rgulr dsruo F s ( F = Fψ = F ( : Φ ϕ F ( ϕ (3 ψ ( ( = = F ( ϕ = [ ψ ( ] ϕ( d = ( [ ψ ( ] ϕ ( Io hs odos u-ouu r ( u osrd from h ssm (5 s dsrd r of rgulr dsruo ( F F for ϕ Φ I suh h rolm of dfo rgrdg h rmrs of h rl ssm (5 rrsd dsruos For xml h rgulr dsruo grd h ouous fuo q /( u (6 s rld o h rmr or s from (5 o h sf s of q ( ϕ = ( ( ( ( ϕ ϕ = ϕ ϕ ϕ Φ = F F F F F If rl (* u * * s rlzo of h modl (5 h h d (3 ks l Fq ( ϕ = F * q* /( u* * ( ϕ = ϕ Φ (3 d rs f u-ouu r ( u* * of h fml of modls (5 h uko rmr grs dsruo Fq ( ϕ = F ( ( ( q /( u * ϕ = F * ϕ F ϕ (35 = hh ssfs Fq ( ϕ = F q /( u* * ( ϕ = ϕ Φ h = * As hs omos s ough hos (ulz f umr N of fudml fuo ϕ = : N d o uld lgr quo F = F (36 hr F s ( N mrx of rl umrs F [ ( ;; ( ;; ( ] = F ϕ F ϕ F ϕn (37 hr -h ro F ( ϕ s g (3 h smol F dos N -olum rl or ul from (3

4 Prodgs of h 7 WSEAS I Cofr o Cllulr & Molulr Bolog - Bohss & Bogrg Ahs Gr Augus 6-7 F [ ( ( ( ] = F ϕ F ϕ F ϕ N (3 Wh ol h rsro ( u of h r ( u o h m rl s ll h o mus hos ϕ suh h su( ϕ = : N If r = rk( F = h uqu soluo s od = ( F F F F = * (39 h hrrhl sruur of dfo d smo quos Cosdr ll s rls ssl for msurms so = ξ h dml ssm (5 ( os rol dds rmrs d msurd rls o o lr quos uko rmrs h dfo rolm s sl srl smlr rlkd dfo rolms lld dfo lrs Bsd o h sf sruur of hs ssm s ossl o grou h s quos suh o drm f rod dfo rolms of h (39 llld Lr_* *= d h r orgzd hrrhl sruur Frs Lr_ som s quos r ulzd o o s of lr quos som rmrs h rsuls of hs frs sg of dfo r ulzd for xrssg ohr rmrs lr quos Lr_ hs ross s rd h ohr lrs ul ll rmrs r dfd For h dfo lr h sm of rodurs d umrl lgorhms r ld Lr_: Idfo of Susug xrsso φ from (5 o (7 o h Lr_ modl (5 q /( u = ( ξ + u3 ξ ( ξ u3 ξ + u u3 ( hrrzd = [ ] = [ ] = ( F ( ϕ = [ ξ ( ] ϕ ( d + [ u ( ξ ( ] ϕ ( F 3 ϕ ( ϕ = [ F ( ] Also F ( ϕ = [ ξ ( ] ϕ ( + [ u ( ξ ( ] ϕ ( [ u ( u ( ] ϕ ( ( ( 3 3 Lr_: Idfo of 5 7 Cosdrg ko = from h Lr_ d susug (6 quo (7 oms ξ ξ ξ = 5 u3 ξ + u u3 7 h Lr_ modl (5 s o q /( u = ( ξ ξ 5 + ( ξ + u3 ξ u u3 7 ( ξ ξ u ξ + u u ξ ( 3 3 hrrzd = [ ] = [ 5 7] = ( F ( ϕ = [ ξ ( ξ ( ] ϕ ( F ( ϕ = [ ξ ( ] ϕ ( [ u( ξ ( ] ϕ ( + [ u ( u ( ] ϕ ( 3 ( 3 ( ; F = F F ( ϕ [ ( ϕ ( ϕ] Also F ( ϕ = [ ξ ( ] ϕ ( ( ( + [ u ( ξ ( ] ϕ ( + [ u ( u ( ξ ( ] ϕ ( 3 3 Lr_: Idfo of 3 Cosdrg ko 5 = 5 ; 7 = 7 from h Lr_ h smd xrsso φ of h rol φ s ξ ξ φ = 5 ( 7 ξ( ξ( hos m xrsso s φ( = 5 7 ( Susug xrsso φ from ( d ( sd of φ o ( o ξ = φ 3 [ ξ3 + u3 ξ3] u3 ξ hh drms h Lr_ modl (5 q /( u = ( φ + ( ξ3 u3 ξ3 3 ( ξ + u3 ξ (3 hrrzd = [ ] = [ 3] = ( F ( ϕ = [ φ ( ] ϕ ( F ( ϕ = [ ξ ( ] ϕ ( d + [ u ( ξ ( ] ϕ ( ( ( ϕ = [ ( ϕ ( ] ϕ ( ϕ = [ ξ ( ] ϕ ( + ( [ u3( ξ( ] ϕ ( d / 6 9 F F F Also F d + Lr_d: Idfo of Cosdrg ko = 3 = 3 from h Lr_ d susug (9 quo ( hr φ s rld φ o ξ3 ξ ξ = φ 3 u ' 3 ξ + 9 ξ h Lr_d modl (5 s o d q /( u = ( ξ3 ξ ( ξ + u3 ξ φ + 3 / + ( ξ ξ + u3 ξ φ ξ 9 ( ξ ξ u3 ξ + φ ξ ( hrrzd d d d d / d = [ 3 ] = [ 6 9] = 3 ( F d ( ϕ = [ ξ ( ξ ( ] ϕ ( 3 3

5 Prodgs of h 7 WSEAS I Cofr o Cllulr & Molulr Bolog - Bohss & Bogrg Ahs Gr Augus F ( ϕ = [ ξ ( ] ϕ ( [ u ( ξ ( ] ϕ ( d + [ ( φ ( ] ϕ ( ( 3 ( d d d d ; F = F F F 3 ( ϕ [ ( ϕ ( ϕ ( ϕ] d ( F ( ϕ = [ ξ ( ] ϕ ( [ u3( ( ] ( ξ ϕ ( + [ ( φ ( ξ ( ] ϕ ( Lr_: Idfo of / / Cosdrg ko = ; = ; = from h Lr d dfo h smd xrsso φ of h olr fuo φ s ξ3 ξ φ = 6 (5 / + 9 ξ hos m xrsso s ξ3( ξ( φ = 6 / ( + 9 ξ ( Susug xrsso (5 sd of φ o ( ξ5 =u3 ξ5 + φ u hh drms h Lr_ modl (5 q /( u = ( φ ( ξ5 + u3 ξ5 + u (6 hrrzd = [ ] = [ ] = ( F ( ϕ = [ φ ( ] ϕ ( F ( ϕ = [ F ( ϕ] Also ( ϕ [ ξ5( ] ϕ ( ; F = + [ u ( ξ (] ϕ ( [ u (] ϕ ( ( ( Exrml rsuls h modl g (5 - ( d h hrrhl dfo rodur dlod hs r hs mlmd Ml hr s of xrms r rformd Nos fr; Cos rmrs u ouu msurms r os omd; 3 Som ross rmrs h rdom ros roud os lus l s of sg fuos ϕ ( hrrzd oudd suor = [ ] < r osdrd All of hs omlsh h odo ϕ ( = ( h ozro rsro s of h form ϕ( = αβ ( Ψ( Φ hr for + Ψ ( = Ψ( C[( ] s o of h four s Exol: Ψ ( = x[ /( ( ] ; Susodl: Ψ ( = s [ π ( /( ] 3 Poloml : Ψ ( = ( ( Produ : Ψ ( = f( f( hr f C [( ] f C [( ] ; + ( k ( f ( = k = : ; f k ( = k = : For h of h four s hr rs mlmd h rs o h off β = β ( Hr α s slg for Fr mlud: β ( = Normlzd k: β ( = /mx Ψ( 6 (=ξ( ξ = S ξ 3 = X ξ = S ξ = X ξ 5 = P m s (=ξ( Normlzd r: β ( = / Ψ( Fg shos h os fr ssm m rsos Fg m rsos for os fr ssm Nos fr dfo rsuls Rl lus Idfd lus For hs dfo 3 sg fuos ϕ ϕ ϕ3of h (susodl-ormlzd r of h dgr = o h rls = (5 = (5 3 = (5 hs ulzd Fg shos h os omd msurd rls ulzd dfo Nos omd dfo ξ = S ξ = S ξ 5 = P ξ = X m s ξ 3 = X Fg Nos omd msurd rls Nos omd dfo Rl lus Idfd lus

6 Prodgs of h 7 WSEAS I Cofr o Cllulr & Molulr Bolog - Bohss & Bogrg Ahs Gr Augus (=ξ( ξ = X ξ = S Fr os dfo ξ = S ξ 5 = P ξ 3 = X m m s Fg3 m rsos for ohr uko rmrs Fr os omd dfo Rl lus Idfd lus Coluso hrough hs rsrh hs rod h s ossl o df ll rmrs of ouous m olr ssms f h r rld o msurd rls rol xrssos hs s ossl f h dfo rolm s formuld s s of rod dfo rolms h lr dds rmrs d msurd rls h rolm of fuols sd dfo oss hs o lzd for rodr lss of olr ssms ACKNOWLEDGMENS hs ork s suord h gr CEEX 6- MENER r 77/P/76 Rfrs: [] Bs G Doh D 99 O-l Esmo d Ad Corol of Borors Elsr [] Bsog Grr H Sll P 997 PMFsd sus mhod for ouous-m modl dfo drms sud Pro of h IFAC Smosum o Ssm Idfo Fukuok Jul [3] Bod S Chu L O 95 Fdg mmor d h rolm of roxmg olr orors h Volrr srs IEEE rs o Crus d Ssms 3( 5-6 [] Horkm B l 996 Idfo of h ouous-m MIMO s s modls Pro of h 35h IEEE Cofr o Dso d CorolKo D [5] Ks W odorsu P 975 Iroduo o dsruo hor h hl los Edur h Buhrs 975 [6] L L M Bllgs S A Couous m o-lr ssm dfo h frqu dom I J Cor Vol7 o [7] Mr C 99 Pross Corol Algorhm UK P Srl No 93353/99 [] Mr C Wood J 993 Arus for d Mhod of Corollg Pross USA P Srl No /6/993 [9] Mr C 999 Ssm Idfo h mhod of ghd moms h Irol Cofr o Corol Ssms d Comur S CSCS Buhrs [] Mr C Ssm Idfo Bsd o Dsruo hor Prodgs of h IASED I Cofr Ald Smulo d Modllg (ASM Cr Ju [] Mr C Pr E Slsu D Sdrsu D 5 Idfo of Nolr Pls Dsruos Alo for Wsr Bodgrdo Pross h 5h I Cofr o Corol Ssms d Comur S - CSCS5 M Buhrs [] Mr C Pr E Slsu D Sdrsu D 5 m r ssm dfo dsruo; Alo for sr odgrdo ross Irol Sm SINES Cro Rom O 5 [3] Ohsum A Kmm K l Sus dfo for ouous-m ssms dsruo-sd roh Auom 3 (63-79 [] V Orsh P D Moor B 996 Sus ssm dfo for lr ssm Boso Klur Adm Prss [5] Pr A Uhu H 995 Idfo of lss of olr ouous m ssms usg Hrl modulg fuos IJCor Vol6 No63-5 [6] Prso A E L F C 95 O h dfo of Poloml u-ouu dffrl ssms IEEE rsaucorvol AC3 No77-7 [7] Pr E Nolr Corol Ssms- Alos Boholog Ursr Cro Rom [] Slşu D Pr E Şdrsu D Modlg d dfo of sr odgrdo ross I Cof SIMSIS Gl No