Rotational Machine Fault Detection with Ensemble Empirical Mode Decomposition Based on a Three Orthogonal Channel Sensor
|
|
- Philip Sharp
- 6 years ago
- Views:
Transcription
1 Rotatonal Machne Fault Detecton wth Enemble Emprcal Mode Decompoton Baed on a hree Orthogonal Channel Senor L an Purdue Unverty North Central lzhetan@pnc.edu Alexander Mua Purdue Unverty North Central Jutn Polng Purdue Unverty North Central Ka Jutce Purdue Unverty North Central Hongbo Xu Nanjng Unverty of Scence and echnology Abtract Rotatonal machne fault detecton and condtonal montorng can prevent harmful envronment and enure relable operaton of equpment. In order to acheve fault detecton and condtonal montorng, many gnal proceng technque, uch a hort-tme Fourer tranform (SFF), wavelet tranform and emprcal mode decompoton (EMD), have been developed. Among thee method, the EMD proce ha been a very promng and effectve technque. h paper propoe an EMD-baed algorthm that cont of two tage. he frt tage procee vbratonal gnal ung three orthogonal channel recordng to obtan a prncpal component gnal. At the econd tage, the enemble emprcal mode decompoton (EEMD) appled to the prncpal component gnal to obtan the ntrnc mode functon (IMF). he Hlbert-Huang tranform pectrum baed on IMF for varou operatng load condton examned for fault dagno. he propoed algorthm allevate the computatonal load by ung the prncpal component gnal ntead of three ndvdual x-, y-, and z-channel recordng. he expermental valdaton of the propoed algorthm are demontrated ung vbraton gnal acqured from a three-phae electrc nducton motor for healthy and fault condton under varou load. Introducton For pat decade, tme-frequency and tme-cale analy method uch a hort-tme Fourer tranform (SF) and wavelet tranform [1-3] have been nvetgated for analy of nontatonary or nonlnear gnal wth applcaton n rotatonal machne fault detecton and health montorng to prevent harmful envronment and enure relable operaton of equpment. Although thee technque are uccefully appled to machne health dagno Proceedng of he 14 IAJC-ISAM Internatonal Conference ISBN
2 and fault detecton, the reult depend on the electon of wndow type or the ue of a bae wavelet. Recently, the Hlbert-Huang tranform (HH) [4,5] ha been propoed to decompoe a gnal nto a et of ntrnc mode functon (IMF) va the emprcal decompoton (EMD) proce [6-1]. he EMD an adaptve approach and effectve to decompoe the non-tatonary or nonlnear gnal (ee detal below). However, the EMD proce uffer from a problem of mode mxng due to gnal ntermttency [11,1]. he problem may caue the decompoed reult vague and napproprately nterpreted. o elmnate the mode mxng problem, the enemble emprcal mode compoton (EEMD) algorthm [11, 1] ha been propoed. h method eentally procee the orgnal gnal wth an added whte noe equence nto a et of IMF ung the tandard EMD repettvely. he enemble mean of the correpondng IMF, whch are obtaned from the tandard EMD, ued a the fnal EEMD decompoed IMF (ee detal n below). Although the EEMD effectve for removng the mxng mode problem, the computatonal load huge due to the enemble proce. Specally, when applyng mult-channel gnal uch a gnal from a enor that provde three-orthogonal channel nformaton, proceng each channel data equence va the EEMD proce requre even more computaton and hnder practcal applcaton. h paper frt decrbe the prncple of the tandard EMD, Hlbert-Huang tranform, and EEMD. o reduce the computatonal load by ung the EEMD for multchannel gnal, a prncpal component emprcal decompoton (PCEEMD) algorthm propoed. he PCEEMD proce cont of two tage: the frt tage contruct the prncpal component gnal baed on the data ened from three-orthogonal channel, and the econd tage apple the tandard EEMD proce to the prncpal component gnal. After obtanng the IMF n the prncpal drecton, they can be drectly employed for rotatonal machne fault detecton by the HH pectrum, or, a an opton, the obtaned IMF can be projected nto three orthogonal axe. Algorthm Development Prncple of EMD, H Spectrum, and EEMD he EMD an adaptve decompoton approach whch appled to decompoe nonlnear and non-tatonary gnal. he EMD proce extract a et of IMF from the orgnal gnal. Each IMF mut meet two condton [4]: the number of extrama and the number of zero crong mut be ether equal or dffer at mot by one; the mean value of the envelope defned by the local maxma and the envelope defned by the local mnma at any pont mut be zero. he tep of the EMD algorthm [4-6] to decompoe a gnal x( t ) decrbed below: Step 1: Intalze r = x and et = Step : Extract the th IMF wth the followng ftng procedure: a. Intalze h ( k 1) = r 1 wth k = 1 Proceedng of he 14 IAJC-ISAM Internatonal Conference ISBN
3 b. Fnd the local maxma and local mnma of gnal h ( ) ( 1) t c. Interpolate the local maxma and local mnma by cubc plne to contruct the upper and lower envelope of h ( ) ( 1) t k d. Calculate the mean m ( ) ( k 1) t of the upper and lower envelope of h ( ) ( k 1) t e. Calculate hk = h ( k 1) m ( k 1) f. If the top crteron for the teraton k gven below atfed [ h ( k 1) hk ] SD (1) h t= ( k 1) where SD a predefned value and uually et to.1, that, f equaton 1 atfed, h ( ) ( k ) t an IMF and then et c = h ( k ) ; ele et k = k + 1 and then go to tep (b). Step 3: Calculate equence: r ( ) ( ) ( ) + 1 t = r t c t Step 4: If r ( ) + 1 t ha at leat extrema then et = + 1 and go to tep ; ele the decompoton completed and r ( ) + 1 t the redual gnal. he decompoton reult are lted below: x c = r By ummng them, t follow that 1 1 r c = r 1.. r ( ) ( ) ( ) N 1 t cn t = rn t N = 1 k x = c + rn () It can be een that gnal x( t ) decompoed nto N ntrnc mode functon and a redue gnal rn ( t ). Once gnal x( t ) decompoed to N IMF, the Hlbert tranform (H) [4,5] can be appled to each of IMF to obtan ntantaneou frequency, that, 1 c y = dτ π (3) t τ he analytcal gnal z ( t ), whch contructed ung both IMF c ( t ) and t H y ( t ), can be expreed a z = c + jy (4) hen the ntantaneou envelope of the analytc gnal for the th IMF found to be a t = c t + y t (5) ( ) ( ) ( ) and the correpondng phae angle can be determned by 1 y θ = tan c (6) Proceedng of he 14 IAJC-ISAM Internatonal Conference ISBN
4 Notce that ntantaneou envelope a ( t ) ndcate the gnal energy varaton whle the phae angle θ the ntantaneou phae. he ntantaneou frequency for the th IMF can be found by takng dervatve of the phae angle, that, dθ ω = (7) dt he Hlbert tranform baed on the IMF referred to Hlbert-Huang tranform (HH); and the tme-frequency plot of HH referred to HH pectrum. Although the EMD demontrate the effectvene n decompong nonlnear and non-tatonary gnal, the method ha a problem of mode mxng; that, a ngle IMF may contan ocllaton of dramatcally dparate cale, or a component of a mlar cale rede n dfferent IMF due to gnal ntermttency. he ntermttence could caue erou gnal alang n tmefrequency dtrbuton a well a make the phycal meanng of the ndvdual IMF unclear. he noe-ated data analy [11, 1] by addng noe to the orgnal gnal propoed. h method referred to the enemble emprcal mode decompoton (EEMD). he prncple of the EEMD can mply be decrbed a follow. he EEMD add whte noe to the orgnal gnal before applyng the EMD. Snce the added whte noe n background populate the whole tme-frequency pace unformly, the gnal component at dfferent cale can automatcally be projected onto proper cale of the reference etablhed by the whle noe n the background. Although each tral may produce noy reult, the noe n the reult can be cancelled out by ung the enemble mean wth a gnfcant number of tral. Hence, each IMF obtaned ung EEMD the enemble mean of tral. he EEMD then ummarzed below: Step 1: Add a whte noe equence to the orgnal gnal (the tandard devaton of noe =1~% of the tandard devaton of the orgnal gnal). Step : Decompoe the gnal wth added whte noe equence nto IMF [ c, at mth tral] ung EMD. Step 3: Repeat Step 1- wth dfferent whte noe equence for M tme Step 4: Calculate the enemble mean for each IMF M 1 c = c, = 1,, L, N (8), m M m = 1 Obvouly, the EEMD algorthm ha a large computatonal load. Development of Prncpal Component EEMD In many applcaton, a enor [13] acqurng gnal may contan mult-component. Fgure 1 depct an accelerometer (ngle taton) contng of three orthogonal x-, y-, and z- channel. Channel x and y are degnated to record acceleraton n x and y drecton, repectvely. Channel z meaure vertcal acceleraton. An ncomng gnal ha angle of α, m Proceedng of he 14 IAJC-ISAM Internatonal Conference ISBN
5 β, and γ relatve to x-, y-, and z-axe, repectvely. Applyng the EEMD algorthm for each channel requre a gnfcant amount of computatonal load. Aumng ( ) Fgure 1. A enor wth x-, y-, z- channel recodng n the ncomng gnal wth a drecton of [ co co co ] Proceedng of he 14 IAJC-ISAM Internatonal Conference ISBN α β γ whle x( n ), y( n ), and z( n ) are the enor recordng, the ncomng gnal can be etmated by a lnear combnaton x( n) ( n) = U X = [ u1 u u 3] y( n) (9) z( n) U u u u X = x( n) y( n) z( n). where = [ ] and [ ] 1 3 Agan, the enor gnal are aumed to be zero mean proce, that, E( x( n)) E ( X ) = E( y( n)) = (1) E( z( n)) then E ( n) = E U X = (11) ( ) ( ) where E ( ) the expectaton operator. Note that the power of the ncomng gnal can be expreed a ( = E ( n) ) = U E ( XX ) U = U CU (1) where C a 3x3 covarance matrx defned below: x xy xz C = E ( XX ) = xy y yz (13) xz yz z x E x ( n) y E y ( n) z = E z ( n), xy = E ( x( n) y( n) ), wth = ( ), = ( ), ( ) = E ( x( n) z( n) ), and E ( y( n) z( n) ) xz =. Baed on Fgure 1, t can be een that yz
6 x( n) coα X = y( n) co β = ( n) z( n) coγ U = coα co β coγ found, the etmated ncomng gnal become If [ ] ( α β γ ) ( n) = U X = co + co + co ( n) = 1 ( n) (15) Equaton 15 ndcate that U [ u u u ] = hould be a untary vector, that, U U = and the bet untary vector the one to maxmze the power of the ncomng gnal wth the followng contrant: max (16) U, λ L ( = U CU λ U U 1) (17) akng dervatve of to U and ettng the reult to zero, t follow that L ( C λ I ) U = (18) akng dervatve of to the Lagrange multpler L λ and ettng the reult to zero, the untary vector contrant U U = 1 yelded. It clear that the Lagrange multpler L C C C eentally an egenvalue of covarance matrx C, that, λ λ1, λ, λ3. o enure be the maxmum value, takng econd-order dervatve of to U lead to the followng Proceedng of he 14 IAJC-ISAM Internatonal Conference ISBN L λ (14) to matrx: L ( C λ I) U L = = C λ I = H (19) U U H H and H mut be em-negatve defnte. Let λ and U an egenvalue and an egenvector of matrx H. Equaton 19) become H L H ( H λ I) U = [ C ( λ + λ ) I] U = () H L H Equaton ndcate that λ + λ an egenvalue of matrx C, that, C L H λ = λ + λ = 1,,3 (1) and U H = U. he egenvalue of matrx H can be determned a H H C L λ = λ λ, = 1,,3 () H L C o enure λ (H mut be em-negatve defnte), λ = λmax. he correpondng untary C vector U for λmax the optmal vector whch repreent the gnal prncpal drecton. Wth the obtaned optmal untary vector of U, the prncpal component gnal acheved a ( n) = U X. herefore, the propoed prncpal component enemble emprcal mode decompoton (PCEEMD) algorthm ummarzed below: Step 1: Compute covarance matrx C.
7 C Step : Determne the maxmum egenvalue λ max and t correpondng untary egenvector U. Step 3: Compute the prncpal component gnal ( n) = U X. Step 4: Apply the EEMD algorthm to the prncpal component gnal ( n) = U X to obtan IMF. Step 5: (optonal) Project IMF to x-, y-, and z-axe, repectvely, that, IMFx = u1 IMF, IMFy = u IMF, IMFz = u3 IMF Experment and Valdaton o valdate the propoed PCEEMD method for non-tatonary or nonlnear gnal analy, vbratonal gnal from the accelerometer baed on three-orthogonal channel were acqured from the three-phae nducton motor wth an adjutable load (Fgure ). A hown n Fgure, an accelerometer wa attached on the three-phae nducton motor. he acceleraton meaured n x-, y-, z- axe were obtaned va LabVew data acquton platform at a amplng rate of 1 khz wth a 16-bt data reoluton. he acqured data equence from each channel wa preproceed to remove t mean (DC component). he adjutable load va the belt wa coupled to the motor va a rubber coupler. A fault n the rubber coupler wa ntroduced. Fgure 3 how healthy and fault coupler condton. he coupler n fault condton ha nner and outer worn-out teeth on the drvng de. he experment were carred out wth no load (% load), medum load (5% load), and full load (1% load) wth the motor runnng at 1,8 rpm. he peed of the haft wa montored by an optcal encoder. Fgure. Expermental etup Proceedng of he 14 IAJC-ISAM Internatonal Conference ISBN
8 Fgure 3. Coupler healthy condton and fault condton Notce that for the healthy condton valdaton experment, the healthy coupler wa ntalled whle for the fault condton valdaton, the healthy coupler wa mply replaced by the fault coupler. It alo aumed that the condton for the healthy coupler or the fault coupler tay the ame durng tetng. he tranton condton between the healthy coupler and fault coupler not condered n th paper and wll be nvetgated n the future. Fgure 4 how x-y-z channel vbraton gnal meaured from the enor a well a the prncpal component gnal produced by the PCEEMD algorthm for the healthy coupler and fault coupler under the 5% load. Proceedng of he 14 IAJC-ISAM Internatonal Conference ISBN
9 x (n) y (n) z (n) (n) me (m) x (n) y (n) z (n) (n) me (m) Fgure 4. Acceleraton meaurement and generated prncpal componenet gnal ( n ) (left: healthy condton; rght: fault condton) he econd tage appled the EEMD algorthm to the prncpal component gnal. he prncpal component gnal wa added wth a whte noe equence wth a Gauan dtrbuton ung % of the tandard devaton of the orgnal gnal. he enemble mean of each IMF calculated ung 5 tral. he acheved correpondng IMF for both healthy and fault condton are gven n Fgure 5 for comparon. It can be een that for both cae, there are no gnfcant evdence of mxng mode. he haft frequency of 3 rev/ can be een n IMF6 for both cae. For the healthy condton, there are 9 IMF but 1 IMF for the fault Proceedng of he 14 IAJC-ISAM Internatonal Conference ISBN
10 condton. I M F I M F I M F 3 I M F 4 I M F 5 I M F 6 I M F 7 I M F 8 I M F 9 I M F I M F I M F I M F I M F I M F I M F I M F I M F I M F 9. me (m) me (m) Fgure 5. Decompoed IMF from two coupler condton ung the PCEEMD algorthm (left: healthy condton; rght: fault condton) he correpondng HH pectra for healthy and fault condton are depcted n Fgure 6. A hown Fgure 6a, the domnant frequency component come from the haft rotaton, that, 3 Hz (rev/ec); and for the fault condton a hown n Fgure 6b, bede the domnant frequency component of the haft rotaton (3 Hz), there appear the fourth harmonc component, rregular pule and hgh frequency noe. A an addtonal valdaton, the dcrete-fourer tranform pectra were calculated and dplayed n Fgure 7. Clearly, the haft frequency component domnant for both healthy and fault condton. Smlarly, the fourth harmonc frequency component become gnfcant n the fault condton. However, the DF pectrum doe not how tme-cale nformaton. Proceedng of he 14 IAJC-ISAM Internatonal Conference ISBN
11 Frequency (Hz) Frequency (Hz) th Harmonc me (m) me (m) Fgure 6. he HH pectra from two coupler condton ung the PCEEMD algorthm (left: Healthy condton; rght: fault condton) DF pectrum DF pectrum Frequency (Hz) Frequency (Hz) 1 1 Fgure 7. DF pectra from two coupler condton ung the PCEEMD algorthm (left: healthy condton; rght: fault condton) Addtonal Reult he valdaton for the % and 1% load alo how the mlar reult a that of the 5% load. he reult are content and ummarzed n able 1. able 1. Reult from HH Spectra Operaton Condton Healthy, % load Faulty, % load Healthy, 5% load Faulty, 5% load Healthy, 1% load Faulty, 1% load Domnant frequency Hgh-order harmonc Not Not Not Irregular pule Not Not Not Proceedng of he 14 IAJC-ISAM Internatonal Conference ISBN Hgh frequency noe Not Not Not
12 Snce the EEMD proce only apple to the prncpal component gnal, the computatonal load gnfcantly reduced. Mot mportantly, nce the prncpal component gnal contan the ened vbraton gnal wth t algned drecton o that the obtaned IMF and HH pectra wll preent mot meanngful nformaton for fault detecton and condtonal montorng. Concluon h paper propoed a prncpal component enemble emprcal decompoton (PCEEMD) algorthm for rotatonal machne fault detecton and condtonal montorng. he algorthm very effectve for proceng data from a ngle taton enor wth x-, y-, and z- enng component. he PCEEMD cont of two tage. he frt tage perform vbratonal gnal enhancement to acheve the prncpal component gnal accordng to three orthogonal channel recordng. Wth the prncpal component gnal, the EEMD algorthm appled to obtan the IMF wth an advantage of mxng mode elmnaton. he Hlbert-Huang tranform pectra are then obtaned for rotatonal machne fault detecton and dagno. he algorthm gnfcantly allevate the computatonal load by proceng the prncpal component gnal ntead of three ndvdual channel recordng. he expermental valdaton of the propoed method are demontrated ung vbraton data acqured from the three-phae electrc motor for healthy and fault condton under varou load. Reference [1] Sath, L. (1998). Short-me Fourer and Wavelet ranform for Fault Detecton n Power ranformer durng Impule et. Proceedng of the Inttute of Electrcal Engneerng, Scence, Meaurement and echnology, 145, [] Wang, C., & Gao, R. (3). Wavelet ranform wth Spectral Pot-Proceng for Enhanced Feature Extracton. IEEE ranacton on Intrumentaton and Meaurement, 5, [3] an, L., & Jang, J. (13). Dgtal Sgnal Proceng: Fundamental and Applcaton. (nd ed.). Amterdam: Elever. [4] Huang, N. E., Zheng, S., & Steven, R. L. (1998). he Emprcal Mode Decompoton Method and the Hlbert Spectrum for Non-Statonary me Sere Analy. Proceedng of Royal Socety of London, A454, [5] Feldman, M. (11). Hlbert ranform n Vbraton Analy. Mechancal Sytem and Sgnal Proceng, 5, [6] Le, Y., Ln, J., He, Z., & Zuo, M. (13). A Revew on Emprcal Mode Decompoton n Fault Dagno of Rotatng Machnery. Mechancal Sytem and Sgnal Proceng, 35, [7] Lu, B., Remenchneder, S., & Xu, Y. (6). Gearbox Fault Dagno Ung Emprcal Mode Decompoton and Hlbert Spectrum. Mechancal Sytem and Sgnal Proceng,, [8] L, R., & He, D. (1, Aprl). Rotatonal Machne Health Montorng and Fault Detecton Ung EMD-Baed Acoutc Emon Feature Quantzaton. IEEE ranacton on Intrumentaton and Meaurement, 61(4), Proceedng of he 14 IAJC-ISAM Internatonal Conference ISBN
13 [9] Yang, W., Court, P. J., avner, & Crabtree, C. J. (11). Bvarate Emprcal Mode Decompoton and It Contrbuton to Wnd urbne Condton Montorng. Journal of Sound and Vbraton, 33, [1] Gao, Q., Duan, C., Fan, H., & Meng, Q. (8). Rotatng Machne Fault Dagno Ung Emprcal Mode Decompoton. Mechancal Sytem and Sgnal Proceng,, [11] Zhang, J., Yan, R., Goa, R., & Feng, Z. (1). Performance Enhancement of Enemble Emprcal Mode Decompoton. Mechancal Sytem and Sgnal Proceng, 4, [1] Yan, R., Zhao, R., & Gao, R. (1, December). Noe-Ated Data Proceng n Meaurement Scence: Part wo. IEEE Intrumentaton and Meaurement Magazne, 15(6), [13] Magotra, N., Ahmed, N., & Chael, E. (1989, January). Sngle-Staton Semc Event Detecton and Locaton. IEEE ranacton on Geocence and Remote Senng, 7(1), Bographe LI AN a profeor wth the College of Engneerng and echnology, Purdue Unverty North Central. He receved the B.S. degree from the Southeat Unverty, Nanjng, Chna, n 1984, and the M.S. degree n Structural Engneerng and the M.S. and Ph.D. degree n Electrcal Engneerng from the Unverty of New Mexco, Albuquerque, n 1987, 1989, and 199, repectvely. Dr. an an IEEE Senor Member nce 1. H reearch nteret nclude the area of dgtal gnal proceng, actve noe control and control ytem, and dgtal communcaton. He co-authored two textbook: Dgtal Sgnal Proceng: Fundamental and Applcaton, nd ed., Elever, 13; and Analog Sgnal Proceng and Flter Degn, Lnu Publcaton, 9. He hold a US patent. He ha erved a an aocate edtor for the Internatonal Journal of Engneerng Reearch and Innovaton, and Internatonal Journal of Modern Engneerng. ALEXANDER MUSSA a enor electrcal engneerng tudent at College of Engneerng and echnology, Purdue Unverty North Central. JUSIN POLING a enor electrcal engneerng tudent at College of Engneerng and echnology, Purdue Unverty North Central. KAI JUSICE a enor electrcal engneerng tudent at College of Engneerng and echnology, Purdue Unverty North Central. HONGBO XU a Ph.D. tudent at the School of Mechancal Engneerng, Nanjng Unverty of Scence and echnology, Nanjng, Chna. He a vtng cholar n prng 14, at College of Engneerng and echnology, Purdue Unverty North Central. Proceedng of he 14 IAJC-ISAM Internatonal Conference ISBN
A Hybrid Nonlinear Active Noise Control Method Using Chebyshev Nonlinear Filter
A Hybrd Nonlnear Actve Noe Control Method Ung Chebyhev Nonlnear Flter Bn Chen,, Shuyue Yu, Yan Gao School of Automaton, Beng Unverty of Pot and elecommuncaton, Beng, 00876, Chna Key Laboratory of Noe and
More informationChapter 11. Supplemental Text Material. The method of steepest ascent can be derived as follows. Suppose that we have fit a firstorder
S-. The Method of Steepet cent Chapter. Supplemental Text Materal The method of teepet acent can be derved a follow. Suppoe that we have ft a frtorder model y = β + β x and we wh to ue th model to determne
More informationDistributed Control for the Parallel DC Linked Modular Shunt Active Power Filters under Distorted Utility Voltage Condition
Dtrbted Control for the Parallel DC Lnked Modlar Shnt Actve Power Flter nder Dtorted Utlty Voltage Condton Reearch Stdent: Adl Salman Spervor: Dr. Malabka Ba School of Electrcal and Electronc Engneerng
More informationAdditional File 1 - Detailed explanation of the expression level CPD
Addtonal Fle - Detaled explanaton of the expreon level CPD A mentoned n the man text, the man CPD for the uterng model cont of two ndvdual factor: P( level gen P( level gen P ( level gen 2 (.).. CPD factor
More informationChapter 6 The Effect of the GPS Systematic Errors on Deformation Parameters
Chapter 6 The Effect of the GPS Sytematc Error on Deformaton Parameter 6.. General Beutler et al., (988) dd the frt comprehenve tudy on the GPS ytematc error. Baed on a geometrc approach and aumng a unform
More informationSpecification -- Assumptions of the Simple Classical Linear Regression Model (CLRM) 1. Introduction
ECONOMICS 35* -- NOTE ECON 35* -- NOTE Specfcaton -- Aumpton of the Smple Clacal Lnear Regreon Model (CLRM). Introducton CLRM tand for the Clacal Lnear Regreon Model. The CLRM alo known a the tandard lnear
More informationHarmonic oscillator approximation
armonc ocllator approxmaton armonc ocllator approxmaton Euaton to be olved We are fndng a mnmum of the functon under the retrcton where W P, P,..., P, Q, Q,..., Q P, P,..., P, Q, Q,..., Q lnwgner functon
More informationStart Point and Trajectory Analysis for the Minimal Time System Design Algorithm
Start Pont and Trajectory Analy for the Mnmal Tme Sytem Degn Algorthm ALEXANDER ZEMLIAK, PEDRO MIRANDA Department of Phyc and Mathematc Puebla Autonomou Unverty Av San Claudo /n, Puebla, 757 MEXICO Abtract:
More informationSmall signal analysis
Small gnal analy. ntroducton Let u conder the crcut hown n Fg., where the nonlnear retor decrbed by the equaton g v havng graphcal repreentaton hown n Fg.. ( G (t G v(t v Fg. Fg. a D current ource wherea
More informationScattering of two identical particles in the center-of. of-mass frame. (b)
Lecture # November 5 Scatterng of two dentcal partcle Relatvtc Quantum Mechanc: The Klen-Gordon equaton Interpretaton of the Klen-Gordon equaton The Drac equaton Drac repreentaton for the matrce α and
More informationMethod Of Fundamental Solutions For Modeling Electromagnetic Wave Scattering Problems
Internatonal Workhop on MehFree Method 003 1 Method Of Fundamental Soluton For Modelng lectromagnetc Wave Scatterng Problem Der-Lang Young (1) and Jhh-We Ruan (1) Abtract: In th paper we attempt to contruct
More information728. Mechanical and electrical elements in reduction of vibrations
78. Mechancal and electrcal element n reducton of vbraton Katarzyna BIAŁAS The Slean Unverty of Technology, Faculty of Mechancal Engneerng Inttute of Engneerng Procee Automaton and Integrated Manufacturng
More informationRoot Locus Techniques
Root Locu Technque ELEC 32 Cloed-Loop Control The control nput u t ynthezed baed on the a pror knowledge of the ytem plant, the reference nput r t, and the error gnal, e t The control ytem meaure the output,
More informationA Novel Approach for Testing Stability of 1-D Recursive Digital Filters Based on Lagrange Multipliers
Amercan Journal of Appled Scence 5 (5: 49-495, 8 ISSN 546-939 8 Scence Publcaton A Novel Approach for Tetng Stablty of -D Recurve Dgtal Flter Baed on Lagrange ultpler KRSanth, NGangatharan and Ponnavakko
More informationA New Fault Diagnosis Method for Planetary Gearbox
Internatonal ournal of Performablty Engneerng, Vol. 2, No. 4, uly 26, pp 389-394 Totem Publsher, Inc., 4625 Stargazer Dr., Plano, Texas 7524, U.S.A A New Fault Dagnoss Method for Planetary Gearbox HAIPING
More informationVerification of Selected Precision Parameters of the Trimble S8 DR Plus Robotic Total Station
81 Verfcaton of Selected Precon Parameter of the Trmble S8 DR Plu Robotc Total Staton Sokol, Š., Bajtala, M. and Ježko, J. Slovak Unverty of Technology, Faculty of Cvl Engneerng, Radlnkého 11, 81368 Bratlava,
More informationImage Processing for Bubble Detection in Microfluidics
Image Processng for Bubble Detecton n Mcrofludcs Introducton Chen Fang Mechancal Engneerng Department Stanford Unverst Startng from recentl ears, mcrofludcs devces have been wdel used to buld the bomedcal
More informationA New Virtual Indexing Method for Measuring Host Connection Degrees
A New Vrtual Indexng Method for Meaurng ot Connecton Degree Pnghu Wang, Xaohong Guan,, Webo Gong 3, and Don Towley 4 SKLMS Lab and MOE KLINNS Lab, X an Jaotong Unverty, X an, Chna Department of Automaton
More informationImprovements on Waring s Problem
Improvement on Warng Problem L An-Png Bejng, PR Chna apl@nacom Abtract By a new recurve algorthm for the auxlary equaton, n th paper, we wll gve ome mprovement for Warng problem Keyword: Warng Problem,
More informationA Quadratic Constraint Total Least-squares Algorithm for Hyperbolic Location
I. J. Communcaton, Network and Sytem Scence, 8,, 5-6 Publhed Onlne May 8 n ScRe (http://www.srpublhng.org/journal/jcn/). A Quadratc Contrant otal Leat-quare Algorthm for Hyperbolc Locaton Ka YANG, Janpng
More informationKEY POINTS FOR NUMERICAL SIMULATION OF INCLINATION OF BUILDINGS ON LIQUEFIABLE SOIL LAYERS
KY POINTS FOR NUMRICAL SIMULATION OF INCLINATION OF BUILDINGS ON LIQUFIABL SOIL LAYRS Jn Xu 1, Xaomng Yuan, Jany Zhang 3,Fanchao Meng 1 1 Student, Dept. of Geotechncal ngneerng, Inttute of ngneerng Mechanc,
More informationThe multivariate Gaussian probability density function for random vector X (X 1,,X ) T. diagonal term of, denoted
Appendx Proof of heorem he multvarate Gauan probablty denty functon for random vector X (X,,X ) px exp / / x x mean and varance equal to the th dagonal term of, denoted he margnal dtrbuton of X Gauan wth
More informationAP Statistics Ch 3 Examining Relationships
Introducton To tud relatonhp between varable, we mut meaure the varable on the ame group of ndvdual. If we thnk a varable ma eplan or even caue change n another varable, then the eplanator varable and
More informationECE559VV Project Report
ECE559VV Project Report (Supplementary Notes Loc Xuan Bu I. MAX SUM-RATE SCHEDULING: THE UPLINK CASE We have seen (n the presentaton that, for downlnk (broadcast channels, the strategy maxmzng the sum-rate
More informationSUBTRACTION METHOD FOR REMOVING POWERLINE INTERFERENCE
SUBTRACTION METHOD OR REMOVING POWERLINE INTERERENCE ROM ECG IN CASE O REQUENCY DEVIATION Georgy Slavtchev Mhov, Ratcho Marnov Ivanov, Chavdar Lev Levkov aculty of Electronc Engneerng and Technologe (ETT),
More informationConfidence intervals for the difference and the ratio of Lognormal means with bounded parameters
Songklanakarn J. Sc. Technol. 37 () 3-40 Mar.-Apr. 05 http://www.jt.pu.ac.th Orgnal Artcle Confdence nterval for the dfference and the rato of Lognormal mean wth bounded parameter Sa-aat Nwtpong* Department
More informationSupporting Information. Hydroxyl Radical Production by H 2 O 2 -Mediated. Conditions
Supportng Informaton Hydroxyl Radcal Producton by H 2 O 2 -Medated Oxdaton of Fe(II) Complexed by Suwannee Rver Fulvc Acd Under Crcumneutral Frehwater Condton Chrtopher J. Mller, Andrew L. Roe, T. Davd
More informationDOA Estimation Method Based on Differential Covariance Matrix
178 JOURNAL OF COMPUERS, VOL. 8, NO. 4, APRIL 213 DOA Etmaton Method Baed on Dfferental Covarance Matr Je Zhou, Guangjun L and Zh Zheng Unverty of Electronc Scence and echnology of Chna/School of Communcaton
More informationOn the SO 2 Problem in Thermal Power Plants. 2.Two-steps chemical absorption modeling
Internatonal Journal of Engneerng Reearch ISSN:39-689)(onlne),347-53(prnt) Volume No4, Iue No, pp : 557-56 Oct 5 On the SO Problem n Thermal Power Plant Two-tep chemcal aborpton modelng hr Boyadjev, P
More informationRolling Bearing Fault Diagnosis Based on EMD-TEO and Mahalanobis Distance
Rollng Bearng Fault Dagnoss Based on EMD-TE and Mahalanobs Dstance Lu Chen, Hu Jameng, Lu Hongme and Wang Jng RLLG BEARG FAULT DAGSS BASED EMD-TE AD MAHALABS DSTACE. LU CHE, HU JAMEG, LU HGME AD WAG JG
More informationChapter Newton s Method
Chapter 9. Newton s Method After readng ths chapter, you should be able to:. Understand how Newton s method s dfferent from the Golden Secton Search method. Understand how Newton s method works 3. Solve
More informationSolution Methods for Time-indexed MIP Models for Chemical Production Scheduling
Ian Davd Lockhart Bogle and Mchael Farweather (Edtor), Proceedng of the 22nd European Sympoum on Computer Aded Proce Engneerng, 17-2 June 212, London. 212 Elever B.V. All rght reerved. Soluton Method for
More information3 Implementation and validation of analysis methods
3 Implementaton and valdaton of anal method 3. Preface When mplementng new method bacall three cae can be dfferentated: - Implementaton of offcal method (nternatonall approved, valdated method, e.g. method
More informationEstimation of Finite Population Total under PPS Sampling in Presence of Extra Auxiliary Information
Internatonal Journal of Stattc and Analy. ISSN 2248-9959 Volume 6, Number 1 (2016), pp. 9-16 Reearch Inda Publcaton http://www.rpublcaton.com Etmaton of Fnte Populaton Total under PPS Samplng n Preence
More informationDigital Simulation of Power Systems and Power Electronics using the MATLAB Power System Blockset 筑龙网
Dgtal Smulaton of Power Sytem and Power Electronc ung the MATAB Power Sytem Blocket Power Sytem Blocket Htory Deeloped by IREQ (HydroQuébec) n cooperaton wth Teqm, Unerté aal (Québec), and École de Technologe
More informationA Hybrid Variational Iteration Method for Blasius Equation
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015), pp. 223-229 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) A Hybrd Varatonal Iteraton Method
More informationElectrical Circuits II (ECE233b)
Electrcal Crcut II (ECE33b) Applcaton of Laplace Tranform to Crcut Analy Anet Dounav The Unverty of Wetern Ontaro Faculty of Engneerng Scence Crcut Element Retance Tme Doman (t) v(t) R v(t) = R(t) Frequency
More informationPythagorean triples. Leen Noordzij.
Pythagorean trple. Leen Noordz Dr.l.noordz@leennoordz.nl www.leennoordz.me Content A Roadmap for generatng Pythagorean Trple.... Pythagorean Trple.... 3 Dcuon Concluon.... 5 A Roadmap for generatng Pythagorean
More informationWeighted Least-Squares Solutions for Energy-Based Collaborative Source Localization Using Acoustic Array
IJCSS Internatonal Journal of Computer Scence and etwork Securty, VOL.7 o., January 7 59 Weghted Leat-Square Soluton for nergy-baed Collaboratve Source Localzaton Ung Acoutc Array Kebo Deng and Zhong Lu
More informationAlpha Risk of Taguchi Method with L 18 Array for NTB Type QCH by Simulation
Proceedng of the World Congre on Engneerng 00 Vol II WCE 00, July -, 00, London, U.K. Alpha Rk of Taguch Method wth L Array for NTB Type QCH by Smulaton A. Al-Refae and M.H. L Abtract Taguch method a wdely
More informationChapter 7 Four-Wave Mixing phenomena
Chapter 7 Four-Wave Mx phenomena We wll dcu n th chapter the general nonlnear optcal procee wth four nteract electromagnetc wave n a NLO medum. Frt note that FWM procee are allowed n all meda (nveron or
More informationPROBABILITY-CONSISTENT SCENARIO EARTHQUAKE AND ITS APPLICATION IN ESTIMATION OF GROUND MOTIONS
PROBABILITY-COSISTET SCEARIO EARTHQUAKE AD ITS APPLICATIO I ESTIATIO OF GROUD OTIOS Q-feng LUO SUARY Th paper preent a new defnton of probablty-content cenaro earthquae PCSE and an evaluaton method of
More informationTeam. Outline. Statistics and Art: Sampling, Response Error, Mixed Models, Missing Data, and Inference
Team Stattc and Art: Samplng, Repone Error, Mxed Model, Mng Data, and nference Ed Stanek Unverty of Maachuett- Amhert, USA 9/5/8 9/5/8 Outlne. Example: Doe-repone Model n Toxcology. ow to Predct Realzed
More informationThe Prncpal Component Transform The Prncpal Component Transform s also called Karhunen-Loeve Transform (KLT, Hotellng Transform, oregenvector Transfor
Prncpal Component Transform Multvarate Random Sgnals A real tme sgnal x(t can be consdered as a random process and ts samples x m (m =0; ;N, 1 a random vector: The mean vector of X s X =[x0; ;x N,1] T
More informationPop-Click Noise Detection Using Inter-Frame Correlation for Improved Portable Auditory Sensing
Advanced Scence and Technology Letters, pp.164-168 http://dx.do.org/10.14257/astl.2013 Pop-Clc Nose Detecton Usng Inter-Frame Correlaton for Improved Portable Audtory Sensng Dong Yun Lee, Kwang Myung Jeon,
More informationThe Order Relation and Trace Inequalities for. Hermitian Operators
Internatonal Mathematcal Forum, Vol 3, 08, no, 507-57 HIKARI Ltd, wwwm-hkarcom https://doorg/0988/mf088055 The Order Relaton and Trace Inequaltes for Hermtan Operators Y Huang School of Informaton Scence
More informationImprovements on Waring s Problem
Imrovement on Warng Problem L An-Png Bejng 85, PR Chna al@nacom Abtract By a new recurve algorthm for the auxlary equaton, n th aer, we wll gve ome mrovement for Warng roblem Keyword: Warng Problem, Hardy-Lttlewood
More informationJoint Source Coding and Higher-Dimension Modulation
Jont Codng and Hgher-Dmenon Modulaton Tze C. Wong and Huck M. Kwon Electrcal Engneerng and Computer Scence Wchta State Unvert, Wchta, Kana 676, USA {tcwong; huck.kwon}@wchta.edu Abtract Th paper propoe
More informationTwo-Layered Model of Blood Flow through Composite Stenosed Artery
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 93-9466 Vol. 4, Iue (December 9), pp. 343 354 (Prevouly, Vol. 4, No.) Applcaton Appled Mathematc: An Internatonal Journal (AAM) Two-ayered Model
More informationENTROPY BOUNDS USING ARITHMETIC- GEOMETRIC-HARMONIC MEAN INEQUALITY. Guru Nanak Dev University Amritsar, , INDIA
Internatonal Journal of Pure and Appled Mathematc Volume 89 No. 5 2013, 719-730 ISSN: 1311-8080 prnted veron; ISSN: 1314-3395 on-lne veron url: http://.jpam.eu do: http://dx.do.org/10.12732/jpam.v895.8
More informationModal Strain Energy Decomposition Method for Damage Detection of an Offshore Structure Using Modal Testing Information
Thrd Chnese-German Jont Symposum on Coastal and Ocean Engneerng Natonal Cheng Kung Unversty, Tanan November 8-16, 2006 Modal Stran Energy Decomposton Method for Damage Detecton of an Offshore Structure
More informationOptimal inference of sameness Supporting information
Optmal nference of amene Supportng nformaton Content Decon rule of the optmal oberver.... Unequal relablte.... Equal relablte... 5 Repone probablte of the optmal oberver... 6. Equal relablte... 6. Unequal
More informationResonant FCS Predictive Control of Power Converter in Stationary Reference Frame
Preprnt of the 9th World Congre The Internatonal Federaton of Automatc Control Cape Town, South Afrca. Augut -9, Reonant FCS Predctve Control of Power Converter n Statonary Reference Frame Lupng Wang K
More informationHongyi Miao, College of Science, Nanjing Forestry University, Nanjing ,China. (Received 20 June 2013, accepted 11 March 2014) I)ϕ (k)
ISSN 1749-3889 (prnt), 1749-3897 (onlne) Internatonal Journal of Nonlnear Scence Vol.17(2014) No.2,pp.188-192 Modfed Block Jacob-Davdson Method for Solvng Large Sparse Egenproblems Hongy Mao, College of
More informationMULTIPLE REGRESSION ANALYSIS For the Case of Two Regressors
MULTIPLE REGRESSION ANALYSIS For the Cae of Two Regreor In the followng note, leat-quare etmaton developed for multple regreon problem wth two eplanator varable, here called regreor (uch a n the Fat Food
More informationTwo Approaches to Proving. Goldbach s Conjecture
Two Approache to Provng Goldbach Conecture By Bernard Farley Adved By Charle Parry May 3 rd 5 A Bref Introducton to Goldbach Conecture In 74 Goldbach made h mot famou contrbuton n mathematc wth the conecture
More informationQuick Visit to Bernoulli Land
Although we have een the Bernoull equaton and een t derved before, th next note how t dervaton for an uncopreble & nvcd flow. The dervaton follow that of Kuethe &Chow ot cloely (I lke t better than Anderon).
More informationA Reference Point-based Precise Relative Positioning Method Using a Single Frequency Receiver
A eference Pont-baed Prece elatve Potonng Method Ung a Sngle Frequency ecever Euho Km, odd Walter, J. Davd Powell, Stanford Unverty BIOGAPHY Euho Km a Ph.D. canddate n the Aeronautc and Atronautc Department
More informationTracking with Kalman Filter
Trackng wth Kalman Flter Scott T. Acton Vrgna Image and Vdeo Analyss (VIVA), Charles L. Brown Department of Electrcal and Computer Engneerng Department of Bomedcal Engneerng Unversty of Vrgna, Charlottesvlle,
More informationMODELLING OF TRANSIENT HEAT TRANSPORT IN TWO-LAYERED CRYSTALLINE SOLID FILMS USING THE INTERVAL LATTICE BOLTZMANN METHOD
Journal o Appled Mathematc and Computatonal Mechanc 7, 6(4), 57-65 www.amcm.pcz.pl p-issn 99-9965 DOI:.75/jamcm.7.4.6 e-issn 353-588 MODELLING OF TRANSIENT HEAT TRANSPORT IN TWO-LAYERED CRYSTALLINE SOLID
More informationThis is a repository copy of An iterative orthogonal forward regression algorithm.
Th a repotory copy of An teratve orthogonal forward regreon algorthm. Whte Roe Reearch Onlne URL for th paper: http://eprnt.whteroe.ac.uk/0735/ Veron: Accepted Veron Artcle: Guo, Y., Guo, L. Z., Bllng,
More informationTensor Analysis. For orthogonal curvilinear coordinates, ˆ ˆ (98) Expanding the derivative, we have, ˆ. h q. . h q h q
For orthogonal curvlnear coordnates, eˆ grad a a= ( aˆ ˆ e). h q (98) Expandng the dervatve, we have, eˆ aˆ ˆ e a= ˆ ˆ a h e + q q 1 aˆ ˆ ˆ a e = ee ˆˆ ˆ + e. h q h q Now expandng eˆ / q (some of the detals
More informationElectric and magnetic field sensor and integrator equations
Techncal Note - TN12 Electrc and magnetc feld enor and ntegrator uaton Bertrand Da, montena technology, 1728 oen, Swtzerland Table of content 1. Equaton of the derate electrc feld enor... 1 2. Integraton
More informationImage Registration for a Series of Chest Radiograph Images
Proceedng of the 5th WE Internatonal Conference on gnal Proceng, Itanbul, Turkey, May 7-9, 006 (pp179-184) Image Regtraton for a ere of Chet Radograph Image Omar Mohd. Rjal*, Norlza Mohd. Noor, hee Lee
More informationTHE VIBRATIONS OF MOLECULES II THE CARBON DIOXIDE MOLECULE Student Instructions
THE VIBRATIONS OF MOLECULES II THE CARBON DIOXIDE MOLECULE Student Instructons by George Hardgrove Chemstry Department St. Olaf College Northfeld, MN 55057 hardgrov@lars.acc.stolaf.edu Copyrght George
More informationUncertainty in measurements of power and energy on power networks
Uncertanty n measurements of power and energy on power networks E. Manov, N. Kolev Department of Measurement and Instrumentaton, Techncal Unversty Sofa, bul. Klment Ohrdsk No8, bl., 000 Sofa, Bulgara Tel./fax:
More informationA Kernel Particle Filter Algorithm for Joint Tracking and Classification
A Kernel Partcle Flter Algorthm for Jont Tracng and Clafcaton Yunfe Guo Donglang Peng Inttute of Informaton and Control Automaton School Hangzhou Danz Unverty Hangzhou Chna gyf@hdueducn Huaje Chen Ane
More informationSTUDY OF A THREE-AXIS PIEZORESISTIVE ACCELEROMETER WITH UNIFORM AXIAL SENSITIVITIES
STUDY OF A THREE-AXIS PIEZORESISTIVE ACCELEROMETER WITH UNIFORM AXIAL SENSITIVITIES Abdelkader Benchou, PhD Canddate Nasreddne Benmoussa, PhD Kherreddne Ghaffour, PhD Unversty of Tlemcen/Unt of Materals
More informationIntroduction to Interfacial Segregation. Xiaozhe Zhang 10/02/2015
Introducton to Interfacal Segregaton Xaozhe Zhang 10/02/2015 Interfacal egregaton Segregaton n materal refer to the enrchment of a materal conttuent at a free urface or an nternal nterface of a materal.
More informationChapter 11: Simple Linear Regression and Correlation
Chapter 11: Smple Lnear Regresson and Correlaton 11-1 Emprcal Models 11-2 Smple Lnear Regresson 11-3 Propertes of the Least Squares Estmators 11-4 Hypothess Test n Smple Lnear Regresson 11-4.1 Use of t-tests
More informationWind - Induced Vibration Control of Long - Span Bridges by Multiple Tuned Mass Dampers
Tamkang Journal of Scence and Engneerng, Vol. 3, o., pp. -3 (000) Wnd - Induced Vbraton Control of Long - Span Brdge by Multple Tuned Ma Damper Yuh-Y Ln, Ch-Mng Cheng and Davd Sun Department of Cvl Engneerng
More informationApplication of the Second-Order Statistics for Estimation of the Pure Spectra of Individual Components from the Visible
Applcaton of the Second-Order Stattc for Etmaton of the Pure Spectra of Indvdual Component from the Vble Hyperpectral Image of her Mture Sung-Ho Jong Yong-U R Kye-Ryong Sn * (Department of Chemtry, Km
More informationAPPROXIMATE FUZZY REASONING BASED ON INTERPOLATION IN THE VAGUE ENVIRONMENT OF THE FUZZY RULEBASE AS A PRACTICAL ALTERNATIVE OF THE CLASSICAL CRI
Kovác, Sz., Kóczy, L.T.: Approxmate Fuzzy Reaonng Baed on Interpolaton n the Vague Envronment of the Fuzzy Rulebae a a Practcal Alternatve of the Clacal CRI, Proceedng of the 7 th Internatonal Fuzzy Sytem
More informationAnalysis of Financial Data Anomaly Based on Data Mining Technology
Revta de la Facultad de Ingenería U.C.V., Vol. 3, N 5, pp. 338-346, 7 Analy of Fnancal Data Anomaly Baed on Data Mnng echnology Qn Xu * School of Economc & Management, Chengdu etle College, Chna *Correpondng
More informationSalmon: Lectures on partial differential equations. Consider the general linear, second-order PDE in the form. ,x 2
Salmon: Lectures on partal dfferental equatons 5. Classfcaton of second-order equatons There are general methods for classfyng hgher-order partal dfferental equatons. One s very general (applyng even to
More informationAGC Introduction
. Introducton AGC 3 The prmary controller response to a load/generaton mbalance results n generaton adjustment so as to mantan load/generaton balance. However, due to droop, t also results n a non-zero
More informationDesign of Recursive Digital Filters IIR
Degn of Recurve Dgtal Flter IIR The outut from a recurve dgtal flter deend on one or more revou outut value, a well a on nut t nvolve feedbac. A recurve flter ha an nfnte mule reone (IIR). The mulve reone
More informationLecture 10 Support Vector Machines II
Lecture 10 Support Vector Machnes II 22 February 2016 Taylor B. Arnold Yale Statstcs STAT 365/665 1/28 Notes: Problem 3 s posted and due ths upcomng Frday There was an early bug n the fake-test data; fxed
More informationMultigradient for Neural Networks for Equalizers 1
Multgradent for Neural Netorks for Equalzers 1 Chulhee ee, Jnook Go and Heeyoung Km Department of Electrcal and Electronc Engneerng Yonse Unversty 134 Shnchon-Dong, Seodaemun-Ku, Seoul 1-749, Korea ABSTRACT
More informationVariable Structure Control ~ Basics
Varable Structure Control ~ Bac Harry G. Kwatny Department of Mechancal Engneerng & Mechanc Drexel Unverty Outlne A prelmnary example VS ytem, ldng mode, reachng Bac of dcontnuou ytem Example: underea
More informationIterative Methods for Searching Optimal Classifier Combination Function
htt://www.cub.buffalo.edu Iteratve Method for Searchng Otmal Clafer Combnaton Functon Sergey Tulyakov Chaohong Wu Venu Govndaraju Unverty at Buffalo Identfcaton ytem: Alce Bob htt://www.cub.buffalo.edu
More informationPHYS 705: Classical Mechanics. Calculus of Variations II
1 PHYS 705: Classcal Mechancs Calculus of Varatons II 2 Calculus of Varatons: Generalzaton (no constrant yet) Suppose now that F depends on several dependent varables : We need to fnd such that has a statonary
More informationA New Inverse Reliability Analysis Method Using MPP-Based Dimension Reduction Method (DRM)
roceedng of the ASME 007 Internatonal Degn Engneerng Techncal Conference & Computer and Informaton n Engneerng Conference IDETC/CIE 007 September 4-7, 007, La Vega, eada, USA DETC007-35098 A ew Inere Relablty
More informationSuppose that there s a measured wndow of data fff k () ; :::; ff k g of a sze w, measured dscretely wth varable dscretzaton step. It s convenent to pl
RECURSIVE SPLINE INTERPOLATION METHOD FOR REAL TIME ENGINE CONTROL APPLICATIONS A. Stotsky Volvo Car Corporaton Engne Desgn and Development Dept. 97542, HA1N, SE- 405 31 Gothenburg Sweden. Emal: astotsky@volvocars.com
More informationOver-Temperature protection for IGBT modules
Over-Temperature protecton for IGBT modules Ke Wang 1, Yongjun Lao 2, Gaosheng Song 1, Xanku Ma 1 1 Mtsubsh Electrc & Electroncs (Shangha) Co., Ltd., Chna Room2202, Tower 3, Kerry Plaza, No.1-1 Zhongxns
More informationA De-Noising Method for Track State Detection Signal Based on the Statistical Characteristic of Noise
Journal of Transportaton Technologes, 204, 4, 327-336 Publshed Onlne October 204 n ScRes. http://www.scrp.org/journal/jtts http://dx.do.org/0.4236/jtts.204.44029 A De-Nosng Method for Track State Detecton
More informationALGORITHM FOR THE CALCULATION OF THE TWO VARIABLES CUBIC SPLINE FUNCTION
ANALELE ŞTIINŢIFICE ALE UNIVERSITĂŢII AL.I. CUZA DIN IAŞI (S.N.) MATEMATICĂ, Tomul LIX, 013, f.1 DOI: 10.478/v10157-01-00-y ALGORITHM FOR THE CALCULATION OF THE TWO VARIABLES CUBIC SPLINE FUNCTION BY ION
More informationPhysics 141. Lecture 14. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 14, Page 1
Physcs 141. Lecture 14. Frank L. H. Wolfs Department of Physcs and Astronomy, Unversty of Rochester, Lecture 14, Page 1 Physcs 141. Lecture 14. Course Informaton: Lab report # 3. Exam # 2. Mult-Partcle
More information2.3 Least-Square regressions
.3 Leat-Square regreon Eample.10 How do chldren grow? The pattern of growth vare from chld to chld, o we can bet undertandng the general pattern b followng the average heght of a number of chldren. Here
More informationComparative Study on Electromagnetic and Electromechanical Transient Model for Grid-connected Photovoltaic Power System
Energy and Power Engneerng, 13, 5, 47-5 do:1.436/epe.13.54b48 Publhed Onlne July 13 (http://www.crp.org/journal/epe) Comparatve Study on and Tranent Model for Grd-connected Photovoltac Power Sytem Man
More informationSome Comments on Accelerating Convergence of Iterative Sequences Using Direct Inversion of the Iterative Subspace (DIIS)
Some Comments on Acceleratng Convergence of Iteratve Sequences Usng Drect Inverson of the Iteratve Subspace (DIIS) C. Davd Sherrll School of Chemstry and Bochemstry Georga Insttute of Technology May 1998
More informationDepartment of Electrical & Electronic Engineeing Imperial College London. E4.20 Digital IC Design. Median Filter Project Specification
Desgn Project Specfcaton Medan Flter Department of Electrcal & Electronc Engneeng Imperal College London E4.20 Dgtal IC Desgn Medan Flter Project Specfcaton A medan flter s used to remove nose from a sampled
More information1 Derivation of Point-to-Plane Minimization
1 Dervaton of Pont-to-Plane Mnmzaton Consder the Chen-Medon (pont-to-plane) framework for ICP. Assume we have a collecton of ponts (p, q ) wth normals n. We want to determne the optmal rotaton and translaton
More information2010 Black Engineering Building, Department of Mechanical Engineering. Iowa State University, Ames, IA, 50011
Interface Energy Couplng between -tungsten Nanoflm and Few-layered Graphene Meng Han a, Pengyu Yuan a, Jng Lu a, Shuyao S b, Xaolong Zhao b, Yanan Yue c, Xnwe Wang a,*, Xangheng Xao b,* a 2010 Black Engneerng
More informationOperating conditions of a mine fan under conditions of variable resistance
Paper No. 11 ISMS 216 Operatng condtons of a mne fan under condtons of varable resstance Zhang Ynghua a, Chen L a, b, Huang Zhan a, *, Gao Yukun a a State Key Laboratory of Hgh-Effcent Mnng and Safety
More informationScroll Generation with Inductorless Chua s Circuit and Wien Bridge Oscillator
Latest Trends on Crcuts, Systems and Sgnals Scroll Generaton wth Inductorless Chua s Crcut and Wen Brdge Oscllator Watcharn Jantanate, Peter A. Chayasena, and Sarawut Sutorn * Abstract An nductorless Chua
More informationEnergy Saving for Automatic Train Control in. Moving Block Signaling System
Energy Savng for Automatc Tran Control n Movng Block Sgnalng Sytem Qng Gu, Xao-Yun Lu and Tao Tang Abtract Wth rapd development of the ralway traffc, the movng block gnalng ytem (MBS) method ha become
More informationSingular Value Decomposition: Theory and Applications
Sngular Value Decomposton: Theory and Applcatons Danel Khashab Sprng 2015 Last Update: March 2, 2015 1 Introducton A = UDV where columns of U and V are orthonormal and matrx D s dagonal wth postve real
More informationColor Rendering Uncertainty
Australan Journal of Basc and Appled Scences 4(10): 4601-4608 010 ISSN 1991-8178 Color Renderng Uncertanty 1 A.el Bally M.M. El-Ganany 3 A. Al-amel 1 Physcs Department Photometry department- NIS Abstract:
More informationStudy on Active Micro-vibration Isolation System with Linear Motor Actuator. Gong-yu PAN, Wen-yan GU and Dong LI
2017 2nd Internatonal Conference on Electrcal and Electroncs: echnques and Applcatons (EEA 2017) ISBN: 978-1-60595-416-5 Study on Actve Mcro-vbraton Isolaton System wth Lnear Motor Actuator Gong-yu PAN,
More information