Fault prediction using the combination of regularized OS-ELM and strong tracking SCKF

Transcription

1 WSEAS RANSACIONS on SYSEMS and CONROL Zhanlong Du, Xaon L, Lpng X, Jnzhong Zhang Fault prdcton usng th cobnaton of rgularzd OS-ELM and strong tracng SCKF ZHANLONG DU *, XIAOMIN LI, LEIPING XI, JINZHONG ZHANG 2. Dpartnt of UAV Engnrng Mchancal Engnrng Collg No. 97 of Hpngxlu, Shjazhuang, 53 P. R. CHINA 2. Councaton ngnrng dsgn and rsarch nsttut of gnral staff Shnyang, P. R. CHINA Abstract: - As on of th ost portant aspcts n antnanc, fault prdcton has attractd an ncrasng attnton for avodng syst catastrophc daag and nsurng rlablty. Consdrng prognoss of unasurd fault paratr n nonlnar syst, a novl forcastng algorth s prsntd basd on th cobnaton of ROS-ELM (rgularzd onln squntal xtr larnng achn) t srs prdctor and SSCKF (strong tracng squar-root cubatur Kalan fltr). ROS-ELM s utlzd to forcast syst asurnts n futur t nstant, whch ar usd by SSCKF as asurnt varabls durng fltr procss. h fadng factor s ntroducd nto th squar root of th SSCKF prdcton rror covaranc to tun th gan atrx. A stat and paratr jont fltr basd on SSCKF s proposd to solv th probl that faulty changng functon s unnown n practc. An xprnt cas s provdd to vrfy th good prforanc of th prsntd approach. Ky-Words: - Strong tracng fltr; Squar-root cubatur Kalan fltr (SCKF); Stat and paratr jont fltr; Onln squntal xtr larnng achn (OS-ELM) ; hr-tan syst; Falur prognoss Introducton Du to ncrasngly hgh rqurnts of syst safty, t s usually rqurd to prdct syst dgradaton trnd bfor a fault has dvlopd to caus syst daag. As a rsult, fault prdcton tchnologs, whch provd axu opratonal avalablty and usag lf for syst, attract uch attnton n antnanc and ndnfcaton, spcally n avoncs, achn and anufactur ndustry flds. h xstng fault prdcton thods can b classfd nto two classs: odl-basd approachs and data-drvn approachs [. In ths papr, a odl-basd thod s dvlopd. Modl-basd approachs usually tnd to b or ffctv and provd good prdctng prforanc, f th fault procss s wll odld [2. Sots th falur can not b obsrvd drctly. Kalan fltr thods, as odl-basd thods, usng syst output asurnts (obsrvabl varabls) to ndrctly stat unasurd fault paratr (hddn varabls), hav bn appld wdly n fault dagnoss [3, 4 and prdcton [5, 6 aras. Rf. [5 utlzd Kalan fltr to forcast otor rotatng spd aftr buldng lnar odl of DC otor. hn t prdctd fault progrsson accordng to dvaton of th forcastd rotatng spd fro th standard rotatng spd. But Kalan fltr s only sutabl to lnar systs. For nonlnar systs, xtndd Kalan fltr (EKF), unscntd Kalan fltr (UKF) and partcl fltr (PF) hav bn proposd squntally. Rf. [6 ployd two sulaton cass to valdat th ffctvnss of EKF n ultpl-stps-ahad fault prdcton. Howvr, owng to just on ordr lnarzaton approxaton prcson for EKF, ts staton rsult ay ntroduc larg rrors and vn dvrgnc ovr t n strong nonlnar syst. hors [7 and xprnts [8 hav provd that UKF statng accuracy s supror to EKF. In Rf. [9, UKF was usd to forcast powr battrs voltag of two-wll lctro-chancal oscllator. hn rsdual usful lf (RUL) was calculatd by th prdctd voltag. Whras UKF xsts llcondtond probl durng updatng covaranc atrx, whch ay lad nvald atrx dcoposton; In addton, UKF, plntng th scald unscntd transforaton, has so E-ISSN: Volu, 25

2 WSEAS RANSACIONS on SYSEMS and CONROL Zhanlong Du, Xaon L, Lpng X, Jnzhong Zhang paratrs to b confrd by xprnc, and thrfor, s dffcult to nsur good staton prforanc for fltrng procss [. PF basd approach was adoptd by achn fault prdcton n Rf. [. Unfortunatly, larg coputatonal burdn, partcls dgnraton and dffculty n slctng portant dnsty functon ar thr an probls for PF. Rcntly, Rf. [2 prsntd squar-root cubatur Kalan fltr (SCKF). By ployng sphrcal ntgral crtron and radal ntgral crtron, SCKF drctly coputs nonlnar transfor an and covaranc of fltr procss. Copard wth EKF and UKF, SCKF outprfors n trs of nonlnar approxaton capablty, staton accuracy and fltrng stablty [3. SCKF provds a novl thod for nonlnar fltr and has bn plntd n fault dtcton [4. h afor-ntond lnar and nonlnar Kalan fltrs hav two wansss for fault prdcton. Frstly, changng functon of th statd fault paratr s unnown n practc, whch ay rsults n slow tracng or vn unabl tracng for fault paratrs. Scondly, syst output asurnts n futur t ar unavalabl, whl fltr approachs nd asurnts to coput fault paratrs. o solv th frst probl, stat and paratr jont staton algorth basd on strong tracng squar-root cubatur Kalan fltr (SSCKF) s prsntd. h proposd SSCKF provs robustnss and guarants good tracng ablty. Also SSCKF ovrcos odl satchng du to unnown changng functon. o th scond probl, th ROS-ELM (rgularzd onln squntal xtr larnng achn) [5 s ployd to forcast asurnts at t nstant + to +n, whr s th currnt t nstant, n s prdcton horzon. Wth th forcastd asurnts. hn SSCKF can prfor fault prdcton. hs papr s organzd as follows. W dscrb th probl statnt of fault prdcton basd on ROS-ELM and SSCKF n Scton 2. h proposd strong tracng SCKF s dscrbd n Scton 3. Scton 4 ntroducs ROS-ELM prdctng odl. In Scton 5, th prsntd fault prdcton thod s gvn. Scton 6 shows xprntal studs for vrfyng th prsntd approach. Fnally, so conclusons ar outlnd n Scton 7. nx z whr x R and z R dnot syst stat and asurnt vctors rspctvly; f () and h () dfn stat functon and asurnt n functon rspctvly; α R α ar syst paratrs, whch ar constant. stat nos w and asurnt nos v ar ndpndnt Gaussan wht nos wth q and r ans, sytrc postv dfntnss covaranc Q and R. Suppos on of th syst paratrs θ bcos faulty. o stat θ basd on stat and paratr jont staton algorth, syst U can b changd by xtndng θ as a stat vctor, x f ( x, θ, ϕ) w x + (3) θ θ d z h( x, θ, ϕ ) + v (4) whr α [ θ ϕ, θ s faulty paratr whl ϕ dnots constant paratrs wthout falur, d s faulty paratr nos. f () and h () dfn stat functon and asurnt functon rspctvly. Futur t asurnts z +, z +2, ar dandd for fltr algorth to stat futur t stats x +, x +2, and fault paratr θ +, θ +2,, thrfor z +, z +2, ar forcastd by ROS-ELM odl to plnt fault prdcton, hr s th currnt t nstant. Fro quaton (3) w can s that paratr θ s no longr constant whn t bcos faulty. hus paratr changng functon θ g ( θ ) s rqurd to buld faulty odl. Howvr, faulty paratr changng trnd s hard to gan n practc,.., functon g () s unnown. In ths cas, assstant stat functon θ θ s ntroducd as th changng functon g () accordng to Rf. [3. h actual changng functon of θ s unnown n quaton (3), whch sgnfcantly ncrass syst uncrtanty. As a rsult, standard SCKF staton accuracy for faulty paratr θ s low. o prov SCKF tracng ablty for θ, a strong tracng SCKF algorth, whch has good robustnss aganst odl uncrtanty, s proposd to stat θ n quatons (3) and (4). h dtal of strong tracng SCKF s dscussd n Scton 3. 2 Probl statnt Consdr th nonlnar dynac dscrt syst U, x ( x, α ) + w () f z h ( x, α ) + v (2) 3 Strong tracng SCKF In ths scton, th strong tracng fltr thory s gvn frstly. hn fadng factor calculaton procdur s dducd basd on thory frawor of strong tracng fltr. Fnally, th dtal algorth of E-ISSN: Volu, 25

3 WSEAS RANSACIONS on SYSEMS and CONROL Zhanlong Du, Xaon L, Lpng X, Jnzhong Zhang SSCKF s gvn accordng to fadng factor calculaton procdur and standard SCKF. 3. Strong tracng fltr thory Convntonal nonlnar fltr algorths (EKF, UKF, SCKF, tc) ar poor n robustnss aganst odl uncrtants and ths dcrass stat staton prcson. Manwhl ths fltr algorths los stat tracng ablty wth unnown stat changng functon. In addton, gan atrx tnds to b nu whn syst rachs stady status. Unl convntonal nonlnar fltr algorths, strong tracng fltrs ntroduc fadng factor λ nto stat pror covaranc atrx P to adjust gan atrx. W obtan E[( x ˆˆ x)( x x ) n (5) E[ ε+ jε,,,, j,2, (6) Equaton (5) s fltr prforanc ndcator, whl quaton (6) forcs output rsdual vctor ε to b orthogonal at ach t nstant. Modl uncrtants ay lad rsdual vctor of convntonal fltrs to b non-orthogonal. hrfor rsdual vctor orthogonalty provs ts robustnss aganst odl satchs and stat tracng capacty. Rf. [6 prsntd strong tracng fltr, hr strong tracng thory s ntroducd nto SCKF to plnt strong tracng SCKF. 3.2 Fadng factor calculaton For dynac dscrt syst coposd of quatons (3) and (4), suboptal fadng factor λ of strong tracng fltr s calculatd by th followng quatons [6. λ λ > tr[ N λ, λ λ tr[ M (7) N V HQ H R (8) M H F P F H (9) εε V ρv + εε 2 + ρ () ε ˆ z z () f h F, xˆˆ x H (2) h abov quatons for λ nd to coput partal drvatvs of stat functon f( ) and asurnt functon h( ) wth rspct to stat x, naly Jacoban atrcs F - and H, as shown n quatons (8) and (9). Howvr, coputng Jacoban atrcs ay b dffcult and rror-pron n hgh ordr nonlnar syst; In addton, t s contrary to th proprty of a drvatv-fr nonlnar Kalan fltr for SCKF [2. hrfor w dduc a drvatv-fr algorth to calculat suboptal fadng factor λ, whch s sutabl for strong tracng SCKF. Bfor ntroducng λ, stat pror covaranc P, output pror covaranc P and crosscovaranc xz, zz, P can b xprssd by {[ ˆˆ [ } E{ [ ˆˆ [ } E{ [ ˆ [ ˆ } P E x x x x (3) P z z z z (4) zz, P x x z z (5) xz, Snc x ˆ x s unrlatd wth asurnt nos v, w obtan P E [ x xˆ [ z zˆ { } {[ x ˆˆ x [ H( x x ) v r } {[ x ˆˆ x [ x x } H xz, E + E P H (6) Q s supposd to b a postv dfntnss covaranc atrx, so nvrs atrx of P xsts. Fro quaton (6) w obtan H [ Pxz, [ P (7) W substtut quaton (7) nto quaton (8), thn N V [ Pxz, [ P Q [ P Pxz, R (8) For F P F n quaton (9), obvously w hav P F P F + Q (9) Substtutng quatons (7) and (9) nto quaton (9), w obtan M HF P F H H( P Q ) H HP H HQ H (2) HP H + R V + N Pzz, V + N Fnally, w substtut N of quaton (8) and M of quaton (2) nto quaton (7) to coput fadng factor λ. E-ISSN: Volu, 25

4 WSEAS RANSACIONS on SYSEMS and CONROL Zhanlong Du, Xaon L, Lpng X, Jnzhong Zhang 3.3 Strong tracng SCKF Undr calculaton quatons of SSCKF suboptal fadng factor λ dducd n Scton 3.2 and standard SCKF flow [2, dtald algorth stps for SSCKF ar as follows. () Intalz stat staton ˆx, covaranc squar-root S, whr (2) updat P S S. Coput th cubatur ponts (,2,,) X ˆ, S ξ + x (2) whr 2n x, n x s stat dnson, ξ s dnotd as follow, 2,, nx 2 ξ (22) n n, 2,, 2 x x + nx + nx 2 whr rprsnts a unt vctor that th th lnt s whl all th othr lnts ar zro. 2Coput th propagatd cubatur ponts(,2,,) γ f ( X ) + q (23),, 3 Coput th pror stat staton xˆ γ, (24) 4 Coput th squar-root of pror rror covaranc bfor ntroducng fadng factor * S ra([ χ SQ, ) (25) * χ ˆˆ [ γ, x γ 2, x (26) γ ˆ, x whr Sra(C) s a trangularzaton opraton to M N atrx C,.., C Q C R C, hr Q C dfns a orthogonal atrx, R C dnots an uppr trangular atrx. h transposd atrx of M M atrx R C s M M slctd, naly S ( R C ). S Q, rprsnts squar-root of stat nos covaranc Q,.., Q SQ, S Q, (3) Coput suboptal fadng factor X ˆ, S ξ + x,, 2,, (27) η, h( X, ) + r,, 2,, (28) zη ˆ, (29) - ( ) P χ χ (3) P χ ( Ζ ) (3) xz, ˆˆ zz, Ζ ( Ζ ) ( ) + P z z R (32) χ ˆˆ [ X, x X2, x (33) X ˆ, x Ζ ˆˆ [ η, z η2, z (34) η ˆ, z Substtutng P of quaton (3), P of - xz, quaton (3) and P zz, of quaton (32) nto quatons (8) and (2), w can obtan fadng factor λ fro th follow quatons. λ λ > tr[ N λ, λ λ tr[ M - N V Ζ ( χ ) Q( χ ) ( Ζ ) R M Ζ ( Ζ ) - V + N (35) whr V s gvn n (). Calculat squar-root of th pror rror covaranc aftr ntroducng fadng factor * S ra([ λ χ SQ, ) (36) (4) Masurnt Updat Coput th cubatur ponts(,2,,) X S ξ + xˆ (37), 2 Coput th propagatd cubatur ponts (,2,,) η h( X ) + r (38),, 3 Coput th pror asurnt aftr ntroducng fadng factor z η, (39) 4 Coput th squar-root of th nnovaton covaranc Szz, ra([ Z S R, ) (4) Ζ [ η, z η2, z (4) η, z whr S R, ar squar-roots of asurnt nos covaranc R,.., R S S R, R, 5 Coput th cross-covaranc atrx P χ Ζ (42) xz, E-ISSN: Volu, 25

5 WSEAS RANSACIONS on SYSEMS and CONROL Zhanlong Du, Xaon L, Lpng X, Jnzhong Zhang χ [ X xˆˆ X x X xˆ, 2,, (43) 6 Coput th gan atrx K ( P / S )/ S (44) xz, zz, zz, 7 h stat postror staton s xˆˆ x + K ( z z ˆ ) (45) 8 Coput squar-root of th rror covaranc S ra([ χ KΖ KS ) (46) R, 4 ROS-ELM Modl Syst asurnts n futur t nstant ar forcastd by ROS-ELM odl. Usng th prognostc asurnts as SSCKF asurnt vctors, th prdctng procss s transford to stat procss n fltr. Extr larnng achn (ELM) wth L hddn nods can b xprssd by th followng quaton L L a f ( µ ) β G(, b, µ ) (47) whr µ n µ δ s nput vctor, β s output n wght, a µ and b ar nput wghts and bass rspctvly, G( a, b, µ ) s an actvaton functon of th th hddn nod wth rspct to nput µ. For addtv hddn nod, G( a, b, µ ) s shown by G( a, b, µ ) g( a µ + b) (48) Gvn N tranng sapls {( µ, )} N δ, hr n µ µ δ and δ dnot nput data and th corrspondng xpctd output rspctvly. h rlatonshp btwn μ and δ s L j a j δ β G(, b, µ ), j,2,, N (49) Rwrt quaton (49) as atrx for, H βτ (5) G( a, b, µ ) G( al, bl, µ ) h Η, G( a, b, µ N) G( al, b L, µ N) N L hn β δ β, Τ (5) L β L δ N N o ovrco th probls of ovr-fttng and sngular atrx for ELM, quaton (5) can b rplacd by sng β through th followng optzaton quaton [5 2 2 n{ H β Τ +λ β } (52) β whr s 2-nor, λ s an postv constant. β can b coputd by [5 ˆ ΤΤ β ( Η Η + λi) Η (53) Rcursv larnng algorth s appld to calculat quaton (53). ROS-ELM can b dscrbd as follows. Stp I. Intalzaton phas. Gvn N ntal tranng sapls ℵ {( µ, )} N δ, th nubr of hddn nods L and actvaton functon g(), N L. () Randoly gnrat nput wghts a and bass b,,2,,l. (2) Coput output atrx H va subttng ℵ {( µ, )} N δ a and b nto quaton (5). (3) Calculat th ntal output wghts β ΤΤ β ( Η Η + λi) Η (54) [ 2 N whr δ δ δ. (4) St. Stp II. Onln squntal larnng phas. () St + whn thr s nw data cong. hn calculat h wth rspct to tranng data ( µ, δ ) by quaton (5). (2) Output wghts β s updatd rcursvly at t nstant accordng to th followng quatons K hhk K K (55) + hk h β β + Kh ( δ hβ ) (56) (3) Go to () of Stp II for nxt t nstant larnng. 5 Fault prdcton Fault prdcton flow can b suarzd as th followng stps Stp Intalzng ROS-ELM. Suppos that asurnt vctor z contan z varabls, naly z [z z 2 z. Each varabl z s prdctd by on ROS-ELM, thus z ROS-ELM odls ar usd,,2,, z. Intalz th th ROS-ELM wth th frst N lngth asurnts { z, } N, whr t t { z, } N ar t t transford nto N pars of nput { z,, z, z } and corrspondng xpctd t, ( p ) t, t, output z t, + rspctvly as tranng data. Hr z,t rprsnts asurnt varabl z at t t nstant, p s bddng dnson. E-ISSN: Volu, 25

6 WSEAS RANSACIONS on SYSEMS and CONROL Zhanlong Du, Xaon L, Lpng X, Jnzhong Zhang Stp 2 Expand fault paratr θ as a nw stat varabl, and thn construct syst as shown n quaton (3) and (4), whr stat vctor s x [ x θ. Fault prdcton procss bgns at N + t nstant. St N +. Stp 3 Forcast z+ : + n [ z+, z+ 2,, z + n at t nstant + to +n by z ROS-ELM odls rspctvly, whr s currnt t nstant, n s prdctng horzon, z + j [ z, + j, z2, + j,, z, z + j ar asurnts, j,2,,n. Multpl-stpsahad asurnts prdcton s procssd by succssvly utlzng on-stp-ahad prdcton. St c. Stp 4 updatng. Coput x ˆ + j + j accordng to quaton (24) and ( S ) + j + j + j + j accordng to quaton (25), whr S s squar-root of pror rror covaranc bfor ntroducng fadng factor. Stp 5 Coput th fadng factor λ + j wth S + j + j by quatons (27) to (35). hn S + j + j s calculatd by quaton (36). Stp 6 Stat postror staton x ˆ + j + j and squar-root of th rror covaranc S + j + j ar coputd accordng to quatons (37) to (46). Stp 7 f c n, st j j +, and thn go to stp 4; ls go to stp 8. Stp 8 Slct ˆ θ + n + n fro x + j + j as prdctd valu of fault paratr. h syst s judgd to b faulty whn ˆ θ + n + n xcds th thrshold. Stp 9 Rturn to stp 3 whn thr s nw cong asurnts and st +. ˆ Vctors n (57) ar dfnd as follows x h x 2 h Q x 2, u Q 2 x 3 h 3 Q3 Q32 Q Ax 2 A, B s A Q 3 Q s 32 whr /2 Q3 azsn sgn( h h3)(2 g h h3 ) /2 Q32 az3sn sgn( h3 h2)(2 g h3 h2 ) (58) /2 Q2 az2sn (2 gh2 ) In quaton (58), sgn( ) s th sgn functon. h paratrs ar st as A s.54 2, S n 5-5 2, Q /s, Q /s, g9.8/s, az.5, az 2.6, az 3.5. Dffrntal functons n quaton (57) can b transford to a dscrt odl by Eulr algorth, thn w obtan x, x f x2, + w x (59) 3, x + t Ax + t B u + w z, x z z 2, x x + v 2 + v (6) z 3, x 3 whr saplng ntrval Δts, w [w,, w 2,, w 3, and v [v,, v 2,, v 3, ar stat and asurnt nos rspctvly. w follow noral dstrbuton N(,. 2 ) and v follow noral dstrbuton N(,.2 2 ). h whol sulaton stps ar 2Δt. h ntal lqud lvl h, h 2.95, h Cas study 6. Sulaton Modl Dscrpton hr-tan syst (DS2) [7 s a wll studd sulaton odl, whch s wdly utlzd n th study ara of fault dagnoss and fault prdcton algorths. In addton, DS2 contans stat and asurnt functon, and ths s convnnt for th applcaton of th proposd SSCKF. As a rsult, DS2 s usd as a sulaton cas to vrfy th ffctvnss of th proposd fault prdcton thod. DS2 s dscrbd as follows dx Ax + Bu dt z [ x x2 x3 (57) 6.2 Sulaton Rsults and Dscusson o valdat th ffctvnss of th proposd thod basd on SSCKF, standard SCKF [2 and SUKF (strong tracng unscntd Kalan fltr) [8 ar usd as th contrastng thods. h frst 5 asurnts z to z 5 ar collctd as ntal tranng sapls for ROS-ELM. hus fault prdcton starts at 5Δt. Sgod addtv functon s chosn as ROS-ELM actvaton functon,.. g( a, b, µ ) /{ + xp[ ( a µ + b)}, whr μ s nput vctor. h nput wghts a and nput bass b ar randoly chosn fro th rang [- and [ sparatly. W st bddng dnson p 3, th nubr of ROS-ELM hddn nods L 5, λ -8. E-ISSN: Volu, 25

7 WSEAS RANSACIONS on SYSEMS and CONROL Zhanlong Du, Xaon L, Lpng X, Jnzhong Zhang Assu that paratr az 2 bcos faulty and t ncrass fro as follows.6 az2, (6) az2, +. (-) > Expand az 2 as a nw stat varabl to construct syst shown n quatons (3) and (4),.., chang th constant paratr az 2 to a t varyng stat az 2,. Suppos th fault changng functon of az 2 (shown n quaton (6)) s unnown n actual. hus assstant stat functon az 2, az 2, s ntroducd as th changng functon. hn quatons (59) and (6) ar transford as, x + t A( az2, ) x + t B u w x + az2, d (62) z, x, z z2, x2, + v (63) z 3, x 3, Frstly, thr ROS-ELM odls ar utlzd for 5-stps-ahad forcastng of asurnts z, z 2 and z 3 rspctvly, as shown n Fgur. z / z / tru prdcton Δt / s (a) z z / tru prdcton Δt / s (c) z 3 Fgur 5-stps-ahad prdcton of asurnts h prdctd to 5-stps ahad asurnts by ROS-ELM ar utlzd as asurnt varabls for SSCKF. 5-stps-ahad prdcton valus and absolut prdcton rror basd on standard SCKF, SUKF and SSCKF ar shown n Fgur 2. SUKF and SSCKF can trac az 2 changng trnd, but SCKF fals to forcast az 2. Bcaus fault changng functon of az 2 s unnown, th syst coposd of quatons (62) and (63) contans hgh uncrtanty. Standard SCKF lacs th ablty to xactly stat fault paratr n such uncrtan syst. In contrast, SUKF and SSCKF hav grat robustnss aganst odl satchng, snc strong tracng fltr ntroducs fadng factor to tun gan atrx, whch s usd to prov tracng ablty for fault paratr. hus th prdcton accuracy of SUKF and SSCKF s hgh. SSCKF fadng factor s shown n fgur 3. h MAE (an absolut rror), RMSE (root an squar rror) and t consung ar shown n abl aftr 5 ts Mont Carlo sulatons. Fro abl w can s that SSCKF prdcton accuracy s supror to SUKF. consung for all th thr thods s alost th sa. az tru SSCKF SUKF SCKF.2 tru prdcton Δt / s (b) z Δt / s (a) Prdcton valus E-ISSN: Volu, 25

8 WSEAS RANSACIONS on SYSEMS and CONROL Zhanlong Du, Xaon L, Lpng X, Jnzhong Zhang Absolut rror of az SSCKF SUKF SCKF 5 Δt / s 5 2 (b) Prdcton rror Fgur 2 5-stps-ahad prdcton rsults of az 2 Fadng factor Δt / s Fgur 3 SSCKF fadng factor abl 5-stps-ahad prdcton rror MAE RMSE consung/s SCKF SUKF SSCKF Accordng to th abov sulaton rsults, ROS- ELM can forcast asurnts wll. Coparng wth SUKF and SCKF, SSCKF prfors bttr than SUKF n prdctng accuracy, and prdctng prcson of SCKF s th lowst. 7 Concluson hs papr has addrssd a novl thod usng rgularzd OS-ELM (ROS-ELM) and strong tracng SCKF (SSCKF) for slow varyng fault prdcton. ROS-ELM forcasts futur t asurnts whch ar ployd by SSCKF for falur prognoss. h approach s llustratd through a sulaton cas study, whch shows that th prdctng accuracy of SSCKF s hghr than standard SCKF and SUKF. h rason for th good prforanc achvd by SSCKF s du to th ntroducd fadng factor, whch provs odl robustnss and ovrcos odl satchng du to unnown fault changng functon. h xprnt rsults ndcat th suprorty of th prforanc capablty of th proposd thod. In th xprnt, only sngl fault paratr s consdrd. h stuaton that ultpl fault paratrs occur sultanty wll b studd n th futur wor. Rfrncs: [ Hac Eun K, Andy C.C. an, Josph Mathw, Byong Kun Cho, Barng fault prognoss basd on halth stat probablty staton, Exprt Syst Appl, Vol.39, 22, pp [2 F. Alrowa, R.B. Gopalun, K.E. Kwo, Fault dtcton and solaton n stochastc nonlnar stat-spac odls usng partcl fltrs, Control Engnrng Practc, Vol.2, 22, pp [3 A.M. Bnoudr, R. Kssas, A. Yahaou, J.C. Buvat, S. Gulla, A hybrd approach to faults dtcton and dagnoss n batch and s-batch ractors by usng EKF and nural ntwor classfr, Journal of Loss Prvnton n th Procss Industrs, Vol.25, 22, pp [4 Farzanh Kara, Javad Poshtan, Majd Poshtan, Dtcton of bron rotor bars n nducton otors usng nonlnar Kalan fltrs, ISA ransactons, Vol.49, 2, pp [5 S. K. Yang, An xprnt of stat staton for prdctv antnanc usng Kalan fltr on a DC otor, Rlablty Engnrng and Syst Safty, Vol.75, 22, pp.3-. [6 Zh J Zhou, Chang Hua Hu, Hong Dong Fan, Jn L, Fault prdcton of th nonlnar systs wth uncrtanty, Sulaton Modllng Practc and hory, Vol.6, 28, pp [7 Son J. Julr, Jffry K. Uhlann, A Nw xtnson of th Kalan fltr to nonlnar systs, h Proc of Arosns: h th Intrnatonal Syposu on Arospac/Dfns Snsng, Sulaton and Controls, 997, Orlando, pp [8 Chowdhary Grsh, Jatgaonar Ravndra, Arodynac paratr staton fro flght data applyng xtndd and unscntd Kalan fltr, Arospac Scnc and chnology, Vol.4, 2, pp.6-7. [9 Davd Chldz, Josph P. Cusuano, A Dynacal Systs Approach to Falur Prognoss, Vol.26, 24, pp.2-8. E-ISSN: Volu, 25

9 WSEAS RANSACIONS on SYSEMS and CONROL Zhanlong Du, Xaon L, Lpng X, Jnzhong Zhang [ Xao Jun ang, Zhn Bao Lu, Ja Shng Zhang, Squar-root quatrnon cubatur Kalan fltrng for spaccraft atttud staton, Acta Astronautca, Vol.76, 22, pp [ Chaochao Chn, Bn Zhang, Gorg Vachtsvanos, Marcos Orchard, Machn Condton Prdcton Basd on Adaptv Nuro Fuzzy and Hgh-Ordr Partcl Fltrng, IEEE ransactons on Industral Elctroncs, Vol.58,No.9, 2, pp [2 Inaran Arasaratna, Son Hayn, Cubatur Kalan Fltrs, IEEE ransactons on Autoatc Control, Vol.54,No.6, 29, pp [3 Xaojun ang, Zhnbao Lu, Jashng Zhang, Squar-root quatrnon cubatur Kalan fltrng for spaccraft atttud staton, Acta Astronautca, Vol.76, 22, pp [4 Xao Gong Ln, Shu Shng Xu, Y Ha X, Mult-snsor Hybrd Fuson Algorth Basd on Adaptv Squar-root Cubatur Kalan Fltr, Journal of Marn Scnc and Applcaton, Vol.2, 23, pp.6-. [5 Huynh Hu rung, Won Yonggwan, Rgularzd onln squntal larnng algorth for sngl-hddn layr fdforward nural ntwors, Pattrn Rcognton Lttrs, Vol.32, 2, pp [6 Dong Hua Zhou, Yu Gng X, Zhong Jun Zhang, Suboptal fadng xtndd Kalan fltrng for nonlnar systs, Control and Dcson, Vol.5,No.5, 99, pp.-6. [7 D. Wang, D.H. Zhou, Y.H. Jn, S. Jo Qn, A strong tracng prdctor for nonlnar procsss wth nput t dlay, Coputrs and Chcal Engnrng, Vol.28, 24, pp [8 Xao Xu Wang, Ln Zhao, Quan X Xa, Yong Hao, Strong tracng fltr basd on unscntd transforaton, Control and Dcson, Vol.25,No.7, 2, pp E-ISSN: Volu, 25