Knowledge Fusion: An Approach to Time Series Model Selection Followed by Pattern Recognition

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1 LA-3095-MS Knwledge Fusin: An Appch t Tie Seies Mdel Selectin Fllwed by Ptten Recgnitin Ls Als N A T I O N A L L A B O R A T O R Y Ls Als Ntinl Lbty is peted by the Univesity f Clifni f the United Sttes Deptent f Enegy unde cntct W-7405-ENG-36.

2 Editedby Pul W.Heniksen,GupCIC- Pepedby ShnHudle,GupNIS-7 Thiswkwssupptedby the U.S.DeptentfEnegy,Oj-lcef Nnplj%tinnd NtinlSecuity. t h e t h ~

3 Knwledge Fusin: An Appch t Tie Seies Mdel Fllwed by Ptten Recgnitin Selectin Ths L. Bu Jes C. Scvel Richd B. Stitttte NATIONAL LABORATORY Ls Als, New Mexic 87545

4 CONTENTS A b s I S n t u 2 B c 2 3 M M Au S l t 4 M G d 5 S u R e f A A E M A p M u x l p A B S G M p u p FIGURES R s e D s e c t l s d s 6 c P f c D s c e i l l f d s 6 c B d g f c 7 4 C b t e 8 e s TABLES C R S E f S M e t5 2 D P t T e S f M A C 9 t e b

5 Knwledge Fusin: An Appch ttie Seies Mdel S F R b S A B T L B J l ChS R B Se h i c t A B T d w d d F 9 te w s e b t D s up h E O N N ns nk f p e e F P T p t s s s ud t u t e e f t i p x T s s l pn f p h g f w iu w e p e t t s i g w T g pt i t e e e t e i h t s t dn p un b B t e el i s t s f p u l eu w c we t n f l W t f l l e i u t n f b s e s u nd ul j b t c w p u A e l ic e c ( d t i e e t 2 p p Rp s l f s e f u eb s p fv n cp f b s p e T e g i l e ut c d t f t e p b e t i t t s k s e d p t i t i t d i R e s. Intductinnd Suy I c ( t f i w i e s w R s il f e p w f un b c Se v i e n i t p d s w i ke et s d qs t cu t s t j t b u s b s e R u n cc i he p w t t u b s t c be c se f l s i u b T d t i l e un w b f s h b sh nu c p N p e e ct b n d t et

6 t p w d i eg d i R Ti c p d st e t t w t b t w d p c d T t w t b e f v g c d g ( T p v ea i v e d F D A T i i i nfs S 2 g s t cs e t s t w u t t w t fe t t s R fi p h t e f g Rg f t v A i ew ne i s g f t e f I s g3 w g f d i v e A W p t v A R s e d d i e i A A I s 4 w d p t e e e pi p d g A B d s t p t t s d ip ec s 2 w e t c e n c S p5 i i vp d s u 2. Bckgund I R 2 w d t p c b e b s p c s v u w e u u h d l f t s t i eh t e f f i c iu e g ( c t s v t As T e s p t ut s t s i bi g e u t e n qt p G p p t p c c ut b j t b ie uf t c s n f t c b t t s s A l e t d w t b w c n f c i d t d s e n T p c b d t t s d p e i e ht i c 7 d sn s l d t l s f i s i u i A et e kn T d f c i d s de w 2n c i n e g c f c T f gc ( n d h g p t t t s t c p ( p i c Th f e c w g t t t s t g T d f c 3d t d t i w e s n t p u2 T vt tc d w p t c i c e b ( e ( F t s t Op dc w n u b Oi s e t c c h t d f t 7 i d s e n i c B t w s v b t ie d s A nh e c nc i b u e i w d ft d p f n t eg c e s - t s f t i p T ep q t g t n w s e hu c te d u l s T g d t t q e d b t iv t f v e dfb b i t f f si t e D c t f ci t g c w uf p db t p g T s b t w f s ( g = B + B f + B f + B l 2 g + e 3 * l* ( g = B + B f + B f + e l 2 * l* ( g = B + B * g + e ( ( g = B + B f + e l * l 2

7 (5) g = B + B f + B g + el 2 (6) g = B + Bl f + B g * + e 2 ( l W t f 2 d p s t e w w s t t i v d p 2 w n e t T g w t f t f f t b g d H w d c t t c n bcid d t t v u s w t d d s t v ic b t t s f T f 7 d s w i w nc f t 2 vlues. de T t s t de b t d i h t sde i d i t t c bd s v t t t l d I t h s f t b d t c d w el e f ct T l v w s t t i s e t hn i t c t i d e c f t F s p t i s ei n f d eh d s w i t x f f t n e h - FIGURE. Residulstnddes.Dtsets-644eclss=tuenddtsets ects.... T f c f t s t d i eb th t ic f d F 2 d t B c f M 3i M i 4 f 7 d e s N s t t B c t p g w e e T sbc f h f t p g i M 3 w. f s f t t d b t c d h s v l c c t e t d t 4 eh v f e 3

8 * Zl 4 6UJ dtscl PltfBlf MdeJgs-BO+B*(puentffld)+e 0 w 60J dtt PltfBfMdelgs- BO+Bl*(winns)+e FIGURE2. Pltsffittedcefficients.Dtsets-644eclss=tue,nddtsets ecls. T c t b w c s eh W t e t t e t s e te ng t v i t s n s s i i t b nn vn i t c T d s e u i e s p p w p is t n p i t e i B uh e d c T s e f 7 d es w t t u i t c s p T t c d w s t d i t le w e b i t v n i t c d T s t I T ull id e n t n p i t T f t f l ui d 2 ie t n p i B i t n 2 e t c s 2 d e f M e i t t s t s e p v T s e h f vt e t i t s e n d p p s w h b b i e g e s t b nt d M h t l s e f t c v e d ( t c M c b p p f c p g c T n b n i 6 w u t p f c t p g c I t nh d p 6 w b u w 3 w u p g c c 4 w u p p f c h 4

9 5 T A Cpisn f Residul Stndd E f Six Mdels.??UUW: M H I & M Q! _ M P P P R e S t E 2 2 R e S t E R e S t E A R f w g p 2 2 A R f w g p A R f w g p

10 Detectin f the Pulse T t t l L i d p l p e w u b g i u t e et l c b b uei t Nl tx e b i d pu i le st t c T f s p w e e l M M M M A g B g C g D g = B + BI f + B f + B 2 g * + e * 3 = B + B f + B l g + e 2* = B + B f + B f + e l 2 * = B + Bl g + e * P w p u f n M A B 6e D w be s- e p t M C n b t t e t s e et d h f T s e t f t i t t v i t ie c c s t v b t p v w n e i e e M C w x u e c f c t p t g c h t l s e te fl et Ap w t i c i t d s T u n t pd d 6h n c t i e t c n s s h I t id w tu e g f c t p t g t c i t v t c n l c w l t. i t t u g c t pi g t 0 e h c i t c w. A i eh te d xt n fb u w t p i t d d n s s d f tu d w u i t i b p T d s i i t s u t f np t c e e t p u B n t p v w e s f e b d w i c e A t c d w e b t v l it lt d w s g e i i T t t d w t u e t c f hp T t et c c t t p p sv t n f i ut p e b t w g v c e t v et te t t sh i s s t t t p I t v i vl t t ce t p b e t i c t b t p A d s c e t np i c s w e f c l s t d w t i nf f s e u W t f M A w u b f g c it f t g M C h h w u f c t f t g M D w u hj g c t f s n t g T s s h l e t f t R hs f t i i l s l t b i eq w z ie n scg v u d f n d T l i i t w ts i t b f t en t n t g t pn t f cs e s i F t3 F 3 s t g c f p v t f h c f t s e v p e 6

11 M B G D e * 8 * * ~ *! *** * s ** * pblt M B F D!H* ** ** 5 pint FIGURE3.Bckgundt:gsndflld. 20 S t w t t t ed t b nf i t p sp v n s i t T t t n e i t g f ds n e e i t s w d A t t p n e i t f c etd i f c w s T t t u t p t bb s e l t i t v F 4 s c ve t f M Ci u s e b t t e nf s P w p i v w t e v i p 6 s T ef i w u ( p ne u d p e t t p t sf -t t e ( p n u c e t f t - ( e p s p u t f c M b p 6 sv w e f ( ( D bt t s d ep i e d ts c ( k p v p e ef O t n t t d t p e p n w e n es l p t c t d w iw t p l w e T f s i c x e u t s t i p x b t t p p et n s c c t k p t d n b s i t c s n us p s t d n T i t u N ep L e T l p y t d w d i t c l 9e s t p w c t t n H t d p w d e l 6%. wi t b 7

12 I ** * ** * * * ** * * 5 0 5! Oints RsidukbefensfnnIinfDt ** * * * * s * * * * I s 5 pints ~ entnsftin FIGURE4. Cpfinfesidulsbefendftetnsftins. E w t t t G w t n h t b pev s i i d p ( l f w n t ie c A i w f t s t e t w p w p h d ci s T i t t u t t u d w n b if H q s d f tb ui t e e l s N L e w d yi e e e vp u T d w d i 4 s 4 c e T it s w u u n t s t t s w t b u t s uw e u t e c f t s b w p f t c e e c t e u t t t s h c i t s w e bn F pe wt e s h i c w g c p hn v i t u Oh t t s c p i p t s w b d n M A u e w u b f g c t f t g M Ch w u f s c t f t g w t t b t s P w p u f n d e e F e s -e v c s es t f t p p e c fs t e w d e f t e f Tx v c s t w u t p ce it h p t q d w d ui b d i f s e T fs euc f t q d D i ( 3ui s c R (

13 w 2 E t c v h f t te v se w t p X ~ t i c u e v f t t s t s w t p T v ~ i t 5 v -d v uf e i t f p T p w d s f M A 6M e C b e w g d p v W e i s t t k f f D e e s t t t s f w 3 u M A C I w t eu h l M C w b d b t di w wi s t p e f t s c t s t e t t e c ( n i t v t s t f f e f M A w w t f M C w 7 B i t v t s t f f e i t d t n e p t n u M A w l t t n uf M C t s u p g w b p i t s d e b t g p el fn i e e t t p H t t n t b t ce w b s T uh d p f t t e s g i T 2 N t tt d e b p e i t p c i t f pw R t t fu p i w s 5 ( p t t d p 3 TABLE 2. Detectin Pbbilities n the Testing Set f Mdels A nd C Mdel Detectin Pbbilities W P W P A 3 c 3 2 i H i e f t i px M C T eps n t e t el t c ( n s ef M A w f vm Csw 6 I i u i t e g c x s p C tt eu f t fn t g T i s t v i t b t gi h t f e c u T t d h 4 w c i4 ew c s tt p i h s b M A t t d w ( 3 b Me C3 w ( 2 8% 4 2 D s t d g e i l d pu s f l e w b f i t l v b n t i d s d n e i di S i t d p t it t p n s hi t l e s I t c i f h ct s f t i l s t u t d D c i fl s e t d s c w t v s ~ t t d w en sn ii e s s i D > k2 (2) 9

14 w h I E ( s t s i E ( y 3 W ~ t t d w t p l i W t s Mt Al c t 6 tp d s c wp M C c 5 ltp d s c T t p s b c e t t p 5 h ehe 4 t w e u t c s 2 t t f c p w b 5 e t t d O t s M C p c w t we v e n i t p M A e f T p d p c b e t s d p p t i b d c e s b t l t b p f i b e e u h p g p g b p f p g t e w t p c t t n t b A t v u b i c v d s e f b d d n i t f e fc t t d s F s f g e p d p t f e b e l n w f t t d p c b s e i ia s R d t g be f w t p t t p e t cp 3. MultiviteMdelingf ARIMASeies A i t i n v e na w b t t nt A p e s i s 2 T w h n h e v A e t e c t f s 2 H t s e t ee t e s u v c f w i t t e v A tp e b t t s V A i we i s e et se t RS i l R 4 f e x e O c c e f t s u n i w t s vp p et u e c S W nt t t s v l w db P G i i t B C ( 5 A t s i i S TR R t l c s d t i t d p d b c I t G l S f i i n is u i t v p n u l b ( i d u i t b V t VV e A d R b d b s t A t pb f D t eb p i i t t d t b e f A t G e l p s pt i c t c v u s w c s t Pe e h s t f g f A i c ( fn kp e v f se e t S A Af e v A p e t s x d p e w c t i p (

15 4. Mdelingf GDt A s d A w t i t g e d t t f R t b f t b d N h b c s c t h e d d s T i p i d t t s et s ft i h t ed h f S p h b t w n ees u v A d l t i v t d s g d l wih v i t f d s I p b S i 2 g y h c t w f v t S y T s t g t b f f p e T w et f t t f d v t g i i A i er u ( t f t t f d v t g i i A T t w cr. s I p, h t g d T A c g lr A v l e n vi s t i p A i n p v t l n e f w t e g n i t t n p e c T b i s s u t b g nb c t t w t l A v H b t A v t e v i t e w v h f b t d s v i l d e b t B n ce f w i e e t u t t n A f i s R i I, p H t b t f t g d w b t u t e e w e l v T c b d u t G l f t s w c b i i i i s h i S T G l ( 5 w d b P Gi i t B e C R li v b u t f t s Wuh h b n c l t t e c l t s s k S i c f v A T d u nf t ig e l i i w f vi A p i b el U t e t f t g g l l v f t i s e l l n l v t t p i H t l k v t t e g e v s n b s c w t p t h b t g b t f t s t gs t e g gd e s l t pu v u i t p i ds F t g u t e s t ib v l t d s t e i h n b e t T l xt f i u te K f ue e e t d d I t ei p c b d s l ip g p s i i t cn l i f f n n t u g c g w f s f b f t g c b e e s e t S A B f p s p e f t g d u E p t f d f u i s f b t pv t s wi b d e s l t u p n T i e n n i t g w f t

16 d t d ep M t si s c i cl n e n p w w u et f t t d Te i n f nv h t g u t e i p u t l ld s s e e ~ Suy T d t t c c e t wc i Rc ( d h c b t p u f R el2 p n t N s e ne e L b c s ( i l t t e v A p b P t t w w t v A eo n s i t e ht ps e n A R n M l R i s c e t N n L e p f s c y cd e c b t s i s d e i p d ed l i A t t t w R w w n t v A H f t p p i e e p s w d n t t v A e w n T t e i h n h er t p v A e s d i A e A fi R Refeences T B J D J H D M R us u t F T S M F b P u R A e t U e S s id B D L A N L L c ( l A k 9 S B T B A C JlD B H D M e J P C S u R S T T t A Z F ha ikv t eu T S w E f t S P L Ae x Nl L L ( A e - A 9 R J D W Applied Mdtivite Sttisticl Anlysis, i S E h ( P e 9 n t P B R D TieSeies: They ndit.fethds, S E ( V e 9 P G S A M ia O t ES B l pq v C W P 9 3

17 AppendixA Exple f Multivite ARIMA Mdeling I A A w i s t p l A u c li pt n l ( G L ( 5 d v iw s i e d f be R i sl A t c 2 t e p RT t f s s t c t s s i p t e n T d w s i S f i w j i t t w s ( ( i t h - ve w x t ed i p L d n t b ( 4n T f e f p i t h e Xlt.7x2t = elf + 5e2t + - T s e f i s M qi f e c il l u p b t p t u i e p i ne nt d c s A i d peb w t d i i ti uf t g e R f f f l v ( G i l S f f i k c u i c f el v ( g B s t w pt s t A i ( e f l M l M i e s b t tp cx e b d f t G l S i t G l w t ib u t e t c iu i f e t v i t c b t c t c t e i t n l l c b c e ti e xc k g s h i T s d w e w ti c v w t s d s T s b w uc i e t t se Evlutin with the del used t siulte dt: > t < I ( t # f e u t f u el l A u t s M w n l v e g - g i n l l i 5 2 k ee. A -0.7 O - O

18 B S s t f t u t n l l i 5s l 5 2 k e e. [,] [,2] R M 4 A R i d = i # t i n i v n s f t d = 2 i # t u i d i d b i A = # b s i t s B = C = N 6 p 4 n c n Evlutin with secnd del f se diensins: # N T i knwn t b t w # > t c l ( t e u u e l s ut M w n l v e g - g i l n l l 2 i 7 k 8 ee. A B - - O S s f f t u t n l l 2 i s l 57 k 8 eee. [,] [,2] R M A i d = i n d = 2 i u A = B = R 4

19 C = N 8 p 4 n c n Cpisn f Mdels: T G l h e t f i t c i tx p t d el c b e T P t i g ft w l t s t s d t v t ut I t tf i e t s c p s s b d p c w i h( p -p - q) d h f s w M i i t n u u i t c t pu q e t n A c l M t i t e s e p e T A i c ( Bn i c k ( f gn c A v ef i d ( R c ( f p e ( G s R s t i b t n l b w d ep f g t i i - e g n p v F i t B t c nf w t t p vs l t t A b p h p t p u I s eb i n d t e t F t w d f p ues i s n b ct w s e s t b A I e t t t b f i d l b t t e e e t s i t n i T l f i c t uj ed k t v n e b f t p v tu f t v nt u b l e ( t ip v i st v k v t t t e e d t p T i b x t ci t p t g f t c e t p t t d A s t i s b f c t t p f f ht s e l d T i t t d t f ef e t W s t ps t f w t d w s g t f f ei t t h p > i n tf t e e tu i s b n p. P - A B G R F i O F F P - P t - n l l i to A - n A I C B n- n I k Cf n e i G - G C V e R - R C n l e F - F P E e i

20 AppendixB Suy f G Mdeling T w h i d s e pt t b g cp f c h t s 2 s M t d s d e h. e i i ct p e d c p T l d s ps d s ( w b s u h ep b p s n T c i g e w t d n O c f n s i t ts n y u s w ws d i t eh b w b T s t b i s c b v t t n ih k s e h s s b w e t n e p u l l c l d e c q f t T s w c i t ug t e n I c e s t n c ut d i t w ew t w c tpi - c l e c b j t t n u G f t f n s e s i n n c n u s v t E t d f u i s f b t pv t s wi e b d t ue p n T is e n nc i t g w d t d ep M t s i si c i h cl i n p w w u et f t t d Te i n t f t g u t e i p u t l ld s A d i s w e t t c f t t p s n s n h d t g t s i d n t b e t g n t e b t g l t p i d e n e T d b b e h b i s S s C c e p e c b # s t i e e di Dt Set N D i f i h l p p i ( n # gr t e s # ( g [ 4 3 v. # t s # V s ( [ 9 ( t s p l# t l t t ( Df cg e

21 ( F i ( g # M # n s e [ 0 $ # c E # de s [ 0. 9 $ V # C f tv e t c # 3. 7 $ # A i c v # n k [ 2 $ # s v t i E p i # n s [ 8 7. $ # n N u t c b. t u [ l f # i 7 u D D wi v g it w n s i t A g g n p t e s l ( g s l i. e [ [ 0. [ $ V $ [ 2 6

22 [ 8 7. [ 7 D D i ei x g g nc g Dt Set 2 N D i i h s p l p e ( s n 2 [ 6 5 v ( g [ ( t s p # ld t l t ( c e2 g e ( F i ( g s e [ 0 [ $ V $ [ 3 2 [ 2 6 [ 7 D D i v g Ti n s i t g g n A p t e s l

23 ( g s 2 i. e [ [ [ $ V $ k [ 3 2 [ 2 6 [ 7 D D i g b p i n g i g - g t A T R n s i t A I p t M ph e s i Dt Set 3 N D w s i t h s p p e ( n g e ( g [ v ( g [ ( t s p # ld t. t ( e g ( F h s g e i ( n g e ( g [

24 v ) ( g [ 9 8 ( t s. p # le t ( v g T ( F i ( g s l e [ 0 [ 0. 9 $ V $ [ 9 9 [ 9 6 [ 6 D D i f T i w f e g g n b ( 3 t A p u t eh t v te. t s s (. t G f pl p b- 0 f w t b bl t d c u eu e j ei ( g s l. i e [ [ [

25 $ V $ [ 9 [ 9 6 [ D D i f i T g g e g w t b ( 2 c t Ae u j i p t h f ( 4 v se s ( s l l. t G F p i g f t f t b - t f t z e h ( g s l i. $ [ d e [ [ $ V $ [ 2 8 [ [ 8 2

26 D D i n g i w A Rg g I n T f b h we g t ( t u s - A p t h f ( 4 v se s ( s l e. t G F p z b- l Dt Set 4 N D w d i t h s pi p e ( n g e ( g [ v ( g [ 2 ( t s. p# D t l i d - t e ( g d b 2 i 3 # s e ( F h s g e i ( n g e ( g [ 7 6 v ( g [ ( t s p # l t e t w s D( g # ( Vdp i i # b c 2 e3 ( F i ( g s 2 e [ 0 [ 0. 9 $ V

27 $ [ [ 2 [ 6 D D si wi v g w e g g s c b ( f n et b 3n -u p h t A p h s s ( l e w s. t G F p z - ( g s 2. i e [ [ [ $ V $ [ [ 2 [ 6 D D i v l t ia w Rt g I g g - eb ( p w f s p e - t 3 h t A p et h s e w s ( i. t G F pl p z - 23

28 ( g s i 2. e [ 2 [ [ 0. 9 $ V (2) ( $ [ [ 0 9 [ 6 D D i t s i t w g pe g n t b ( w f t 3 t A e p t - u h t h s b t s e ( i ps l b t G F p s z - ( S h s g e e I ( n g e ( g [ v ( g [ ( t s p # l d t t t l D( g # b c 5 5 e 24

29 (c) F i ( g s e [ 0 [ 0. 9 $ V $ [ [ [ D D si wi v g l eb g g s t ( w f t 3 h t A p -t u w h s s (. e t G F l s p p z - v e ( g s 2 i. e [ [ - 0. [ $ V

30 $ [ [ [ 8 D D i v s ti A w Rt g i I g n s b ie t p l s p ue i ( g s i 2. e [ 2 [ [ 0. 9 $ V l e7 5 0 $ [ [ [ 8 D D i v s ti t t b g i g n t A p t h s s s e( l s l l. s g G e F p b s - t s z t e 26

31 Dt Set 5 N D w d i f h s pi p ( n g e ( g [ v ( g [ 0 5 ( t s p # l t i w t d s D( g b n s u i h s # e ( F h s pg p i e ( n g e ( g [ 8 0 v. j u ( l [ 3 0 ( t s p l# T d h s t V ( g ( F i ( g s l e [ 0 [ 0. 9 $ V $ [ 7 9 [

32 [ 6 D D i n g Afi t g g e g n b ( [ n b t b f d s t - w s t s i t A p t ( i p h e l. t G F p i z b - 2 ( g n s l i. e [ [ [ $ V $ [ 7 9 [ [ 6 D D i n v g i T n v g e g n b ( f g t - 4 b t A p t h e s ( l. t G F p p i z b - t 28 ( g s i l. e [ 2 [

33 [ 0. 9 $ V (2) $ [ 7 8 [ [ D D i n g T i i g e dg t t A R I M ( S h s p g e p e I ( n g e ( g [ 7 6 v. j u l ( [ ( t s p l# t d n st u i ( t g # g i d w w # b A s f d u i ( F i ( g s l $ [ 0 d e [

34 $ V $ [ 9 5 [ [ 8 D D i n g T i l g b t g e g n A p t h s (. e t l ps l G F p i z - e ( g s l. i j e [ [ [ $ V $ [ 9 5 [ [ 8 D D i n b i t ip t ( g e g n f n 4 b t A t h s ( e e l. t G F p i z b - 3

35 ( g s i l. e [ 2 [ [ 0. 9 $ V $ [ 9 5 [ [ 8 D D i t s i w t A g R p g ( T h s gp p I h e ( n g e ( g [ 6 6 v. j u ( l [ ( t s p l# d t n ( D g ( F i ( g s l e [ 0 3

36 [ 0. 9 $ V $ [ 9 3 [ 2 9 [ 8 D D i n g T i s t g e eg n t ( t A p t h s -( e l 4. t G F p i z b - ( g s l. i j e [ [ [ $ V $ [ 9 3 [ 2 7 [ 8 32

37 D D i n v g i - v s t t g ig A R I M ( F p s g e I ( n g e ( g [ 5 9 V s l. j [ ( t s p l# s d dt ( t g e ( F i ( g s l e [ 0 [ 0. 9 $ V $ [ 7 [ 8 0 [ 6 D D i n p i b T t l g e g ( i n t b t e A p h w s e v s s (. h t G l F p e b p i z - g ev ( g s l. i e [ 33

38 [ [ $ v $ [ 7 [ 7 9 [ 6 D D i t s ti A R g Ig n Dt Set6 N T d w i h s p l ep ( n g e ( g [ 8 v ( g [ 9 ( t. s # S. t e p l l t v l # w p ( F i ( g s e [ 0 [

39 $ V $ [ 6 3 [ 0 4 [ 6 D D i n v g i T f w g e g f w g t ( t A p u t h - h t e s t (. ht G Fp pl i b z e ( g s l i e [ [ - 0. [ $ V $ [ 6 2 [ 0 3 [ 6 35

40 D D i n g T i f w g e g n s t 4 ( t n esu t u e t v A p t h s t ( e. h ps l l t G F p i z - e ( g i s l e l [ [ 0 e l [ [ e l [ 0. 9 e l [ [ 0 e l [ [ 5 e l [ [ $ V. 4 9 $ [ 6 9 [ 6 0 [ 6 D T i f g w l e w g s n u g t 4 t A p t h s l 6e s w t G F p g ft g - i d c t d t z e u s t e

41 Dt Set 7 N D i i h s p l p e ( n g e ( g [ v ( g [ ( t s. p# D t l w w p t e ( g ( F i ( g n e [ 0 [ 0. 8 $ V $ [ 7 7 [ [ 6 D D i n g T i n b w g e g b w ( t A p t h v i -e e l s t (. th G F p l p i z - e v ( g s 2 i e [ 3

42 [ [ $ V $ [ 7 5 [ 2 5 [ 6 D D i s b i i t t w l g e e g n t A T R b I ( ew M e s f t b e t su t ea p t g e t h v l s t e ( - h s p l b w i b t p t G e h e F p i z - e v ( g i s 2 e l [ [ 0 e l [ [ e l [ 0. 9 e l [ [ 0 38

43 $ [ 2 ] ] [ 5 $ [ 2 ] ] [ $ V. 6 8 $ [ 7 5 [ [ 6 D T i b ( ew f g e s n ( 4 t b e s t A e p t e g h s l 6 w e - t s p G F p i z - Dt Set 8 N D w d i t h s p i p ( n g e ( g [ v ( g [ ( t. s # D. t w V p el n ( F h s g e i ( n g e ( g [ v. n ( t [ ( t. s #. t w V p D n l - 39

44 ( F i ( g n s e [ 0 [ 0. 8 $ V $ [ [ 4 3 [ 6 D D i n v g i T f g e g n ( t A p t h v l - s t e h 3 s (. t G F pl z b- ( g s l i. e [ [ 0. 4 [. 4 6 $ V

45 $ [ [ 4 0 [ 6 D T i s b t iet A l g R s e n w c b ( w b ( nte - -t e i A p h v l s ( e. t sl p l G F p z - v e ( g si l. e l [ 0 $Odel[[lll$ndiff: [ e [ 0. 9 e l [ 0 e l [ 5 f ~ ~ $ V. 5 $ [ 2 [ 8 9 4

46 [ 6 D T i h f e f ( t g u s n A p t h s l 6 w e s l - t G F p f t z t f l. - ( S h s g e e I ( n g e ( g [ v ( g n [ ( t. s # D. V i d p n e l- ( F i ( g n s e [ 0 [ 0. 8 $ v $ [ 2 7 [ 2 5 [ 7 D T i b ( w e t 4 ge - s n u t A p t h v l s t e s p l (. t G F pl i z b 3-42

47 ( g s l. i e [ [ 0. 3 [ $ V $ [ 2 7 [ 2 4 [ 7 D T i b ( ew l g e s n- l t 4 t A p t h s w t e i ps (. t G F pl z b- ( g si l. $ l ] ] [ 0 $ l ] ] [ e [ $del[[2]]: e l [ 0 43

48 e l [ [ 5 e l [ $ v. 8 4 $ [ [ 6 9 [ 7 D T i w e i t g us p n s h t s T A p h e s e e l 6 w h t G F p i fh g t d c t f t z l e u b Dt Set 9 Nte: D w d i t h s p i p e ( n g e ( g [ v ( g [ 8 2 ( t s. # pd t l V p t e ( g- # d ( F h s g e i ( n g e ( g [ 8 4 v ( g [

49 ( t s. p# l V e t ( - gt ( F i ( g s 2 e [ 0 [ 0. 7 $ v $ [ 2 5 [ [ 6 D T i v g t A p e t g s e n h l s t (. th G F p l p z - v e ( g s 2 i. e [ [ 0. 5 [ $ v

50 $ [ 2 4 [ 2 9 [ 6 D D li i i t t A d g R l g n b t s i t A p t g t w p i e i p ( g si 2. e l [ 0 e l [ e [ 0. 9 e l [ 0 e l [ [ 5 e l [ $ v. 7 $ [ 2 4 [

51 [ 6 D T il f g w ce t g s un - t A p h n s l e t i s p s l 6 w - l 3 p g. t G F p z - ( S h s g e e I ( n g e ( g [ v ( g n [ ( t s #. t nw Vp D l t - ( c ) ( g n s $ [ 0 d e [ 0. 8 $ v $ [ [ 9 5 [ 7 D T il v g w e t - t g s u n A p t h l s t e ( h s p l l. t G F p z

52 ( g s 2 i. e [ [ [ $ v $ [ [ 9 3 [ 7 D D i i i t A ( d Rg l g I n s i t A p s s - p e. l s ( g si 2. e l [ 0 e l [ e [ 0. 9 e l [ 0 4

53 e l [ [ 5 e l [ $ V $ [ [ 2 3 [ 7 D R l i f g w e t - t A g s u n p t h s e - l 6 t s l p G F p z - gv Dt Set 0 N D i f i h l p p i ( n g e ( g [ 4 6 v. ( [ 6 5 ( t s p l # 2 c t g s ( g F # n t b l j # t T l l s (c) F i ( g s l e [ 0 49

54 e [ [ 0. 8 $ V $ic: [ 3 5 [ 3 0 [ 7 D T i b ( ew v l g e s n- n t e t s t n su i t A p e t ep h t t G F pe i b t d c s - i f t e s e n ( g s l. i e [ [ e [ [ $ V $ [ 3 5 5

55 [ 3 0 [ 7 D T il l t A e dr g s I n t A p t t G F pe i l t s - l t p e ( g is l. e [ 2 [ e [ [ 0. 9 $ V (2) () (l) (2) () $ [ 3 5 [ 2 9 [ 7 D T p ti b ed t g p s n A p t h t G e F p i s l - t d c f t e s T e t b ut b e n p s f t t h h 5

56 U e t f t g l s e ( U e e v t fl g x s e i Dt Set N G c w t e c g l g A - O B c= n l l i k ee R M 4 4. :39 D T i l v g u tel t pg w ss n n w l b t k e t d s n ie e e c z t p ue t ht s t wn ee - h p e f t f w i - ( px s p i i w p. p u t p h s i f t p ( s p l i hl s N T A v f t t p c n b c s t n i n t s b u i s T c b i b i t p l b f u t lp h b e e v li f t g x T e s ei i l i t l g - u ( A w e e vr l x e ( U c e t f c h gl s eh

57 ( e l e c t g A l - O L l - O. O L 2 - B c= O. O 4 l l l - O. O O 2 6 O 7 L l - O n l l 2 i s l 45 k 2 eee. R M e b e V s A t i t. s = 6 s nd = 8 ( p. t t s d s u= 6( d = g8 t A R i d = i n d = i u A = 6 B = O p C = 5 2 n c n D T ip l v g u t l e f g s n t s w t i f l e h uh u b t k e t d s v ie e s t p n c l t t l z t Ae p t i n h f s t b e w t l h e s p g. t P A p t h v g e s s l 5 p ( U t c e t f c h l s h g ( e l e c t 3 A - L B 53

58 c= 0 - O O L L 5. 3 L n l l 2 i s l 44 k 2 eee. R 3 M e b e s s tt i S S 2 S 3 n e e e p t s d s u= 6( d g8 t A R i d = 3 i n d = i u A = 6 B = O C = 5 2 p 2 n c n D T p ti l g f t f 3 e g s t d t s t f h v l l t u u b t k d t i l l n e s e t d c z i t A p t se h t e ne c s t b t s ( e p g e l. t v s s l 5 t P A p h s s t b e l 5 e s p l l 5 C t t h p i n f. e. t l i s e. l e sc b n p d i P - A B G R F i O F F F

59 P - P t - n l l i to A - n A I C B n - n B I k fc n e i G - G C V e R - R C n l e F - F P E e i d T d t b f e e c T i t su t f c t e d w u h t l c e f t f t e t h H t v v c i b c I w f t i t d w w l t c d w f t d w hn b d hdwi d w if i b b t f c e h l i 5

60 56

61 T h b f t b c I i t D D c f t O S T I P BOX6 O R T 3 P f ( 5 I is t t p f t N T I S U D C 5 P R R S V 2 p e

62 . NATIONAL A LABORATORY Ls Ais, New Mexic 87545

63 Ls Als N A T I O N A L L A B O R A T O R Y Ls Als, New Mexic 87545

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