A Method for Damping Estimation Based On Least Square Fit
|
|
- Brice Todd
- 5 years ago
- Views:
Transcription
1 Amerca Joural of Egeerg Research (AJER) 5 Amerca Joural of Egeerg Research (AJER) e-issn: p-issn : Volume-4, Issue-7, pp Research Paper Ope Access A Method for Dampg Estmato Based O Least Square Ft Jtao Gu, Mepg Sheg School of Mare Scece ad Techology, Northwester Polytechcal Uversty, P. R. Cha Abstract: A ew approach based o least square ft method s proposed to estmate dampg. Nose resstace of the proposed method ad half-power badwdth method are aalyzed ad compared by plety of smulatos wth dfferet sgal-to-ose ratos (SNR). The proposed method s more accurate ad stable tha half-power badwdth method all SNRs, especally whe the ose level s hgh. If SN R 3dB, the proposed method should be used for dampg estmato stead of half-power badwdth method. A dampg estmato expermet s carred out wth both methods, ad the results dcate ad verfy that there s smaller varablty for the proposed method. Keywords: Least square ft, dampg estmato, half-power badwdth I. INTRODUCTION Sce dampg s a valuable parameter for resoat respose of structures or systems, dampg s of great sgfcace for structural dyamcs. It s dffcult to obta dampg through a theoretcal method so that the uversal way for dampg estmates s expermetal vestgato[,]. alf-power badwdth method[3,4], whch calculates resoat dampg wth frequecy badwdth for vbrato eergy decreases 3dB ad the resoat frequecy, s a wdely used approach for dampg estmato. alf-power badwdth method s troduced as ma method for dampg estmates the Amerca test stadard ASTM E Bertha [5] obtaed dampg of a system that does ot possess real modes wth half-power badwdth method. Guo [6] mproved the half-power badwdth method ad proposed a ew method based o tegral opo. Badsar [7] determed the materal dampg rato shallow sol layers wth the half-power badwdth method. As the half-power badwdth method uses oly three data pots, ts accuracy wll be affected by the sgal-to-ose rato (SNR). Whe some of the three data pots are serously affected by ose, a large error wll appear ad caot be eglected. The am of ths work s to put forward a ew method whch has hgh accuracy ad strog ose resstace by usg the ampltude of frequecy respose. II. ALF-POWER BANDWIDT METOD A wdely used method, amely half-power badwdth method, s troduced as follows. The dampg loss factor ca be obtaed by the quotet of half-power badwdth ad the resoat frequecy, as show equato (). The dagrammatc sketch of the method s show Fg.. f alf-power Badwdth f () f Fg.. alf-power badwdth method w w w. a j e r. o r g Page 5
2 Dmesoless ampltude Amerca Joural of Egeerg Research (AJER) 5 The half-power badwdth method s a classcal ad wdely used method, but there s a fatal short comg that f the sgal-to-ose rato (SNR) s ot hgh eough. It s dffcult to recogze the half-power badwdth, see Fg Fg.. alf-power badwdth method wth low SNR It ca be see Fg. that the half-power badwdth s hard to decde because there are more tha two frequeces related to half-power respose. III. DAMPING ESTIMATION BASED ON LEAST SQUARE FIT The parameter of dampg s ofte estmated wth data ear the resoat frequecy. The wdely used half-power badwdth method for dampg vestgato oly uses three data pots of frequecy respose so that t wll cause a large error whe the expermetal data s affected by ose. It s expected to obta a more accurate dampg f more data pots of frequecy fucto are used. Therefore, a ew approach based o least square ft method s proposed whch a umbers of data pots ear resoat frequecy are used. The ampltude of frequecy fucto s F K () where F s exctato force, K the stffess, atural crcle frequecy, ad the loss factor. It s obvous that the maxmum ampltude ca be obtaed m ax F (3) K The dmesoless ampltude s defed as = = m ax Rewrte equato (4) as = Make that x ad y f x x (6), (7) (5) (4) A umber of data pots x, y,,, ca be obtaed accordg to the expermetal frequecy respose. The resdual error s defed as Dmesoless frequecy w w w. a j e r. o r g Page 6
3 Dmesoless ampltude Amerca Joural of Egeerg Research (AJER) 5, (8) err y f x The dampg detfcato ca be trasferred to gettg a proper value of to make the resdual error the most mmum. Gauss-Newto teratve method s used to fd the optmal parameter of dampg. Expad f x, to Taylor seres at pot of tal value as,, ', f x f x f x (9) where f ' x, d f Rewrte equato (8) as x,. d, ', () err y f x f x y g x where y y f x, g x,, g x, f ' x,. Equato () s a typcal least square optmzato problem. The estmated ca be obtaed for the frst geerato by solvg equato (). T T () A A A b where,,,,,, T, b y, y,..., y A g x g x g x. After s obtaed, wll be replaced by ad repeat the above step to get the estmated value for the secod geerato. The terato wll be fshed f the dfferece betwee the eghbor geeratos of s small eough for satsfactory demad. The last geerato of s the estmated dampg. The expermetal ad fttg respose are show Fg. 3 ad dampg ca be obtaed the fttg process expermetal respose fttg respose Fg. 3. Expermetal ad fttg respose IV. RESISTANCE TO NOISE Ths smulato s coducted to llustrate the ose sestvty of the proposed methods. A sgledegree-of-freedom system s adopted to verfy the valdty of least square ft method. A comparso s made betwee least square ft method ad half-power badwdth method. Gaussa radom ose s appled to the smulated frequecy respose, ad the sgal-to-ose rato (SNR) s defed as where S N R lo g sgal ose s ampltude of effectve sgal ad s ampltude of ose. s g a l o s e The smulated sgal parameters are., f 5 z, = f,ad f. z. It s smulated o samples wth the SNR the rage from db to 5 db. Errors of estmated dampg wth the two methods are show Fg. 4. I Fg. 5, each method s tested for 4 ose levels, whch s from db to 5dB wth db terval, wth samples each ose level. The average error s calculated by equato (3). a v e rag e erro r N N Dmesoless frequecy ex act ex act (3) where s the detfed dampg, s the exact loss factor set the smulato, N s the umber e x a c t of samples. w w w. a j e r. o r g Page 7 ()
4 Error% error% error% Amerca Joural of Egeerg Research (AJER) (a) (b) Fg. 4. Error of the estmated dampg versus SNR: (a) proposed method, (b) half-power badwdth method. 4 alf-power badwdth Proposed method Fg. 5. Average error for the two methods It ca be see Fg. 4 that detfed dampg by the two methods are more ad more accurate wth the creased SNR. The accuracy of proposed method s more tha half-power badwdth method at all SNRs. It may also be otced that there s cosderable varablty of half-power badwdth method especally the lower SNR. As see Fg. 5, both methods are of satsfed accuracy f SN R 3dB. But f SN R 3dB, error of half-power badwdth s much larger tha proposed method. It s clear that the proposed method should be used to estmate dampg stead of half-power badwdth f SN R 3dB V. EXPERIMENT The expermet s carred out o a alloy beam wth the dmesos of.3m.m. m, as show Fg. 6. Fg. 7 s the dmesoless respose of the thrd mode. Fg. 5 s the estmated dampg obtaed from sx repeat expermet results by the two methods. Mult-aalyzer Vbrato excter Electroc amplfer Accelerometer specme Power amplfer Fg. 6. Expermetal setup w w w. a j e r. o r g Page 8
5 Dampg Normalzed Ampltude Amerca Joural of Egeerg Research (AJER) Frequecy (z) Fg. 7. Dmesoless respose alf-power Proposed method Fg. 8. Dampg estmated by the two methods As see Fg. 8, t s clear that there s smaller varablty for the proposed method tha half-power badwdth method. Thus, dampg estmated by the proposed method s more accurate tha half-power badwdth method. VI. CONCLUSION A oval method based o least square ft s proposed to estmate dampg ths paper. There s smaller varablty for the proposed method tha half-power badwdth method. The proposed method s more accurate tha half-power badwdth method, especally the lower SNR crcumstaces. The proposed method should be used stead of half-power badwdth method for dampg estmato f SN R 3dB. REFERENCE [] O. Guasch. A drect trasmssblty formulato for expermetal statstcal eergy aalyss wth o put power measuremets. Joural of Soud ad Vbrato, 33(5),, [] M. Rak, M. Ichchou, ad J. olck-szulc. Idetfcato of structural loss factor from spatally dstrbuted measuremets o beams wth vsoelastc layer. Joural of Soud ad Vbrato, 3(4), 8, 8-8. [3] G. A. Papagaopoulos, ad G. D. atzgeorgou. O the use of the half-power badwdth method to estmate dampg buldg structures. Sol Dyamcs ad Earthquake Egeerg, 3(7),, [4] P. W. Wag, W. W. Zhog, ad J. F. su. Ivestgato of mult-layer sadwch beams through sgle degree-of-freedom trasformato. Appled acoustcs, 74(4), 3, [5] B. A. Olmos, ad J. M. Roesset. Evaluato of the half-power badwdth method to estmate dampg systems wthout real modes. Earthquake Egeerg & Structural Dyamcs. 39(4),, [6] Z. W. Guo, M. P. Sheg, J. G. Ma, ad W. L. Zhag. Dampg detfcato frequecy doma usg tegral method. Joural of Soud ad Vbrato, 338(3), 5, [7] S. A. Badsar, M. Scheveels, W. aegema, ad G. Degrade. Determato of the materal dampg rato the sol from SASW tests usg the half-power badwdth method. Geophyscal Joural teratoal, 8(3),, w w w. a j e r. o r g Page 9
best estimate (mean) for X uncertainty or error in the measurement (systematic, random or statistical) best
Error Aalyss Preamble Wheever a measuremet s made, the result followg from that measuremet s always subject to ucertaty The ucertaty ca be reduced by makg several measuremets of the same quatty or by mprovg
More informationAnalysis of Variance with Weibull Data
Aalyss of Varace wth Webull Data Lahaa Watthaacheewaul Abstract I statstcal data aalyss by aalyss of varace, the usual basc assumptos are that the model s addtve ad the errors are radomly, depedetly, ad
More informationComparing Different Estimators of three Parameters for Transmuted Weibull Distribution
Global Joural of Pure ad Appled Mathematcs. ISSN 0973-768 Volume 3, Number 9 (207), pp. 55-528 Research Ida Publcatos http://www.rpublcato.com Comparg Dfferet Estmators of three Parameters for Trasmuted
More informationLecture Notes Types of economic variables
Lecture Notes 3 1. Types of ecoomc varables () Cotuous varable takes o a cotuum the sample space, such as all pots o a le or all real umbers Example: GDP, Polluto cocetrato, etc. () Dscrete varables fte
More informationESS Line Fitting
ESS 5 014 17. Le Fttg A very commo problem data aalyss s lookg for relatoshpetwee dfferet parameters ad fttg les or surfaces to data. The smplest example s fttg a straght le ad we wll dscuss that here
More informationIntroduction to local (nonparametric) density estimation. methods
Itroducto to local (oparametrc) desty estmato methods A slecture by Yu Lu for ECE 66 Sprg 014 1. Itroducto Ths slecture troduces two local desty estmato methods whch are Parze desty estmato ad k-earest
More informationPGE 310: Formulation and Solution in Geosystems Engineering. Dr. Balhoff. Interpolation
PGE 30: Formulato ad Soluto Geosystems Egeerg Dr. Balhoff Iterpolato Numercal Methods wth MATLAB, Recktewald, Chapter 0 ad Numercal Methods for Egeers, Chapra ad Caale, 5 th Ed., Part Fve, Chapter 8 ad
More informationEconometric Methods. Review of Estimation
Ecoometrc Methods Revew of Estmato Estmatg the populato mea Radom samplg Pot ad terval estmators Lear estmators Ubased estmators Lear Ubased Estmators (LUEs) Effcecy (mmum varace) ad Best Lear Ubased Estmators
More informationSimulation Output Analysis
Smulato Output Aalyss Summary Examples Parameter Estmato Sample Mea ad Varace Pot ad Iterval Estmato ermatg ad o-ermatg Smulato Mea Square Errors Example: Sgle Server Queueg System x(t) S 4 S 4 S 3 S 5
More informationL5 Polynomial / Spline Curves
L5 Polyomal / Sple Curves Cotets Coc sectos Polyomal Curves Hermte Curves Bezer Curves B-Sples No-Uform Ratoal B-Sples (NURBS) Mapulato ad Represetato of Curves Types of Curve Equatos Implct: Descrbe a
More informationChapter 2 - Free Vibration of Multi-Degree-of-Freedom Systems - II
CEE49b Chapter - Free Vbrato of Mult-Degree-of-Freedom Systems - II We ca obta a approxmate soluto to the fudametal atural frequecy through a approxmate formula developed usg eergy prcples by Lord Raylegh
More informationBlock-Based Compact Thermal Modeling of Semiconductor Integrated Circuits
Block-Based Compact hermal Modelg of Semcoductor Itegrated Crcuts Master s hess Defese Caddate: Jg Ba Commttee Members: Dr. Mg-Cheg Cheg Dr. Daqg Hou Dr. Robert Schllg July 27, 2009 Outle Itroducto Backgroud
More informationAnalysis of Lagrange Interpolation Formula
P IJISET - Iteratoal Joural of Iovatve Scece, Egeerg & Techology, Vol. Issue, December 4. www.jset.com ISS 348 7968 Aalyss of Lagrage Iterpolato Formula Vjay Dahya PDepartmet of MathematcsMaharaja Surajmal
More informationModule 7: Probability and Statistics
Lecture 4: Goodess of ft tests. Itroducto Module 7: Probablty ad Statstcs I the prevous two lectures, the cocepts, steps ad applcatos of Hypotheses testg were dscussed. Hypotheses testg may be used to
More informationSummary of the lecture in Biostatistics
Summary of the lecture Bostatstcs Probablty Desty Fucto For a cotuos radom varable, a probablty desty fucto s a fucto such that: 0 dx a b) b a dx A probablty desty fucto provdes a smple descrpto of the
More informationCubic Nonpolynomial Spline Approach to the Solution of a Second Order Two-Point Boundary Value Problem
Joural of Amerca Scece ;6( Cubc Nopolyomal Sple Approach to the Soluto of a Secod Order Two-Pot Boudary Value Problem W.K. Zahra, F.A. Abd El-Salam, A.A. El-Sabbagh ad Z.A. ZAk * Departmet of Egeerg athematcs
More informationd dt d d dt dt Also recall that by Taylor series, / 2 (enables use of sin instead of cos-see p.27 of A&F) dsin
Learzato of the Swg Equato We wll cover sectos.5.-.6 ad begg of Secto 3.3 these otes. 1. Sgle mache-fte bus case Cosder a sgle mache coected to a fte bus, as show Fg. 1 below. E y1 V=1./_ Fg. 1 The admttace
More informationChapter 14 Logistic Regression Models
Chapter 4 Logstc Regresso Models I the lear regresso model X β + ε, there are two types of varables explaatory varables X, X,, X k ad study varable y These varables ca be measured o a cotuous scale as
More informationComparison of Dual to Ratio-Cum-Product Estimators of Population Mean
Research Joural of Mathematcal ad Statstcal Sceces ISS 30 6047 Vol. 1(), 5-1, ovember (013) Res. J. Mathematcal ad Statstcal Sc. Comparso of Dual to Rato-Cum-Product Estmators of Populato Mea Abstract
More informationA New Family of Transformations for Lifetime Data
Proceedgs of the World Cogress o Egeerg 4 Vol I, WCE 4, July - 4, 4, Lodo, U.K. A New Famly of Trasformatos for Lfetme Data Lakhaa Watthaacheewakul Abstract A famly of trasformatos s the oe of several
More informationAhmed Elgamal. MDOF Systems & Modal Analysis
DOF Systems & odal Aalyss odal Aalyss (hese otes cover sectos from Ch. 0, Dyamcs of Structures, Al Chopra, Pretce Hall, 995). Refereces Dyamcs of Structures, Al K. Chopra, Pretce Hall, New Jersey, ISBN
More informationDerivation of 3-Point Block Method Formula for Solving First Order Stiff Ordinary Differential Equations
Dervato of -Pot Block Method Formula for Solvg Frst Order Stff Ordary Dfferetal Equatos Kharul Hamd Kharul Auar, Kharl Iskadar Othma, Zara Bb Ibrahm Abstract Dervato of pot block method formula wth costat
More informationLecture 07: Poles and Zeros
Lecture 07: Poles ad Zeros Defto of poles ad zeros The trasfer fucto provdes a bass for determg mportat system respose characterstcs wthout solvg the complete dfferetal equato. As defed, the trasfer fucto
More informationBayes Interval Estimation for binomial proportion and difference of two binomial proportions with Simulation Study
IJIEST Iteratoal Joural of Iovatve Scece, Egeerg & Techology, Vol. Issue 5, July 04. Bayes Iterval Estmato for bomal proporto ad dfferece of two bomal proportos wth Smulato Study Masoud Gaj, Solmaz hlmad
More informationStatistics MINITAB - Lab 5
Statstcs 10010 MINITAB - Lab 5 PART I: The Correlato Coeffcet Qute ofte statstcs we are preseted wth data that suggests that a lear relatoshp exsts betwee two varables. For example the plot below s of
More informationFREQUENCY ANALYSIS OF A DOUBLE-WALLED NANOTUBES SYSTEM
Joural of Appled Matematcs ad Computatoal Mecacs 04, 3(4), 7-34 FREQUENCY ANALYSIS OF A DOUBLE-WALLED NANOTUBES SYSTEM Ata Cekot, Stasław Kukla Isttute of Matematcs, Czestocowa Uversty of Tecology Częstocowa,
More informationRandom Variables and Probability Distributions
Radom Varables ad Probablty Dstrbutos * If X : S R s a dscrete radom varable wth rage {x, x, x 3,. } the r = P (X = xr ) = * Let X : S R be a dscrete radom varable wth rage {x, x, x 3,.}.If x r P(X = x
More informationA Study of the Reproducibility of Measurements with HUR Leg Extension/Curl Research Line
HUR Techcal Report 000--9 verso.05 / Frak Borg (borgbros@ett.f) A Study of the Reproducblty of Measuremets wth HUR Leg Eteso/Curl Research Le A mportat property of measuremets s that the results should
More informationLecture 12 APPROXIMATION OF FIRST ORDER DERIVATIVES
FDM: Appromato of Frst Order Dervatves Lecture APPROXIMATION OF FIRST ORDER DERIVATIVES. INTRODUCTION Covectve term coservato equatos volve frst order dervatves. The smplest possble approach for dscretzato
More informationArithmetic Mean and Geometric Mean
Acta Mathematca Ntresa Vol, No, p 43 48 ISSN 453-6083 Arthmetc Mea ad Geometrc Mea Mare Varga a * Peter Mchalča b a Departmet of Mathematcs, Faculty of Natural Sceces, Costate the Phlosopher Uversty Ntra,
More informationABOUT ONE APPROACH TO APPROXIMATION OF CONTINUOUS FUNCTION BY THREE-LAYERED NEURAL NETWORK
ABOUT ONE APPROACH TO APPROXIMATION OF CONTINUOUS FUNCTION BY THREE-LAYERED NEURAL NETWORK Ram Rzayev Cyberetc Isttute of the Natoal Scece Academy of Azerbaa Republc ramrza@yahoo.com Aygu Alasgarova Khazar
More informationLecture 3. Sampling, sampling distributions, and parameter estimation
Lecture 3 Samplg, samplg dstrbutos, ad parameter estmato Samplg Defto Populato s defed as the collecto of all the possble observatos of terest. The collecto of observatos we take from the populato s called
More informationMultiple Choice Test. Chapter Adequacy of Models for Regression
Multple Choce Test Chapter 06.0 Adequac of Models for Regresso. For a lear regresso model to be cosdered adequate, the percetage of scaled resduals that eed to be the rage [-,] s greater tha or equal to
More informationConfidence Intervals for Double Exponential Distribution: A Simulation Approach
World Academy of Scece, Egeerg ad Techology Iteratoal Joural of Physcal ad Mathematcal Sceces Vol:6, No:, 0 Cofdece Itervals for Double Expoetal Dstrbuto: A Smulato Approach M. Alrasheed * Iteratoal Scece
More informationVOL. 3, NO. 11, November 2013 ISSN ARPN Journal of Science and Technology All rights reserved.
VOL., NO., November 0 ISSN 5-77 ARPN Joural of Scece ad Techology 0-0. All rghts reserved. http://www.ejouralofscece.org Usg Square-Root Iverted Gamma Dstrbuto as Pror to Draw Iferece o the Raylegh Dstrbuto
More information2C09 Design for seismic and climate changes
2C09 Desg for sesmc ad clmate chages Lecture 08: Sesmc aalyss of elastc MDOF systems Aurel Strata, Poltehca Uversty of Tmsoara 06/04/2017 Europea Erasmus Mudus Master Course Sustaable Costructos uder atural
More informationConvergence of the Desroziers scheme and its relation to the lag innovation diagnostic
Covergece of the Desrozers scheme ad ts relato to the lag ovato dagostc chard Méard Evromet Caada, Ar Qualty esearch Dvso World Weather Ope Scece Coferece Motreal, August 9, 04 o t t O x x x y x y Oservato
More informationLecture 7. Confidence Intervals and Hypothesis Tests in the Simple CLR Model
Lecture 7. Cofdece Itervals ad Hypothess Tests the Smple CLR Model I lecture 6 we troduced the Classcal Lear Regresso (CLR) model that s the radom expermet of whch the data Y,,, K, are the outcomes. The
More information1 0, x? x x. 1 Root finding. 1.1 Introduction. Solve[x^2-1 0,x] {{x -1},{x 1}} Plot[x^2-1,{x,-2,2}] 3
Adrew Powuk - http://www.powuk.com- Math 49 (Numercal Aalyss) Root fdg. Itroducto f ( ),?,? Solve[^-,] {{-},{}} Plot[^-,{,-,}] Cubc equato https://e.wkpeda.org/wk/cubc_fucto Quartc equato https://e.wkpeda.org/wk/quartc_fucto
More informationUNIT 2 SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS
Numercal Computg -I UNIT SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS Structure Page Nos..0 Itroducto 6. Objectves 7. Ital Approxmato to a Root 7. Bsecto Method 8.. Error Aalyss 9.4 Regula Fals Method
More informationX ε ) = 0, or equivalently, lim
Revew for the prevous lecture Cocepts: order statstcs Theorems: Dstrbutos of order statstcs Examples: How to get the dstrbuto of order statstcs Chapter 5 Propertes of a Radom Sample Secto 55 Covergece
More informationis the score of the 1 st student, x
8 Chapter Collectg, Dsplayg, ad Aalyzg your Data. Descrptve Statstcs Sectos explaed how to choose a sample, how to collect ad orgaze data from the sample, ad how to dsplay your data. I ths secto, you wll
More informationLong blade vibration model for turbine-generator shafts torsional vibration analysis
Avalable ole www.ocpr.co Joural of Checal ad Pharaceutcal Research, 05, 7(3):39-333 Research Artcle ISSN : 0975-7384 CODEN(USA) : JCPRC5 Log blade vbrato odel for turbe-geerator shafts torsoal vbrato aalyss
More informationFunctions of Random Variables
Fuctos of Radom Varables Chapter Fve Fuctos of Radom Varables 5. Itroducto A geeral egeerg aalyss model s show Fg. 5.. The model output (respose) cotas the performaces of a system or product, such as weght,
More informationResearch on Fault Tolerance for the Static Segment of FlexRay Protocol
Research o Fault Tolerace for the Statc Segmet of FlexRay Protocol Ru I a, Ye ZHU a, Zhyg WANG b a Embedded System & Networkg aboratory, Hua Uversty, Cha b the School of Computer, Natoal Uversty of Defese
More informationBayes Estimator for Exponential Distribution with Extension of Jeffery Prior Information
Malaysa Joural of Mathematcal Sceces (): 97- (9) Bayes Estmator for Expoetal Dstrbuto wth Exteso of Jeffery Pror Iformato Hadeel Salm Al-Kutub ad Noor Akma Ibrahm Isttute for Mathematcal Research, Uverst
More information12.2 Estimating Model parameters Assumptions: ox and y are related according to the simple linear regression model
1. Estmatg Model parameters Assumptos: ox ad y are related accordg to the smple lear regresso model (The lear regresso model s the model that says that x ad y are related a lear fasho, but the observed
More informationMOLECULAR VIBRATIONS
MOLECULAR VIBRATIONS Here we wsh to vestgate molecular vbratos ad draw a smlarty betwee the theory of molecular vbratos ad Hückel theory. 1. Smple Harmoc Oscllator Recall that the eergy of a oe-dmesoal
More informationUnimodality Tests for Global Optimization of Single Variable Functions Using Statistical Methods
Malaysa Umodalty Joural Tests of Mathematcal for Global Optmzato Sceces (): of 05 Sgle - 5 Varable (007) Fuctos Usg Statstcal Methods Umodalty Tests for Global Optmzato of Sgle Varable Fuctos Usg Statstcal
More information2006 Jamie Trahan, Autar Kaw, Kevin Martin University of South Florida United States of America
SOLUTION OF SYSTEMS OF SIMULTANEOUS LINEAR EQUATIONS Gauss-Sedel Method 006 Jame Traha, Autar Kaw, Kev Mart Uversty of South Florda Uted States of Amerca kaw@eg.usf.edu Itroducto Ths worksheet demostrates
More informationMultiple Regression. More than 2 variables! Grade on Final. Multiple Regression 11/21/2012. Exam 2 Grades. Exam 2 Re-grades
STAT 101 Dr. Kar Lock Morga 11/20/12 Exam 2 Grades Multple Regresso SECTIONS 9.2, 10.1, 10.2 Multple explaatory varables (10.1) Parttog varablty R 2, ANOVA (9.2) Codtos resdual plot (10.2) Trasformatos
More informationEstimation of Stress- Strength Reliability model using finite mixture of exponential distributions
Iteratoal Joural of Computatoal Egeerg Research Vol, 0 Issue, Estmato of Stress- Stregth Relablty model usg fte mxture of expoetal dstrbutos K.Sadhya, T.S.Umamaheswar Departmet of Mathematcs, Lal Bhadur
More informationto the estimation of total sensitivity indices
Applcato of the cotrol o varate ate techque to the estmato of total sestvty dces S KUCHERENKO B DELPUECH Imperal College Lodo (UK) skuchereko@mperalacuk B IOOSS Electrcté de Frace (Frace) S TARANTOLA Jot
More informationInvestigation of Partially Conditional RP Model with Response Error. Ed Stanek
Partally Codtoal Radom Permutato Model 7- vestgato of Partally Codtoal RP Model wth Respose Error TRODUCTO Ed Staek We explore the predctor that wll result a smple radom sample wth respose error whe a
More informationSimple Linear Regression
Statstcal Methods I (EST 75) Page 139 Smple Lear Regresso Smple regresso applcatos are used to ft a model descrbg a lear relatoshp betwee two varables. The aspects of least squares regresso ad correlato
More informationDynamic Analysis of Axially Beam on Visco - Elastic Foundation with Elastic Supports under Moving Load
Dyamc Aalyss of Axally Beam o Vsco - Elastc Foudato wth Elastc Supports uder Movg oad Saeed Mohammadzadeh, Seyed Al Mosayeb * Abstract: For dyamc aalyses of ralway track structures, the algorthm of soluto
More informationA New Method for Decision Making Based on Soft Matrix Theory
Joural of Scetfc esearch & eports 3(5): 0-7, 04; rtcle o. JS.04.5.00 SCIENCEDOMIN teratoal www.scecedoma.org New Method for Decso Mag Based o Soft Matrx Theory Zhmg Zhag * College of Mathematcs ad Computer
More informationChapter 5 Properties of a Random Sample
Lecture 6 o BST 63: Statstcal Theory I Ku Zhag, /0/008 Revew for the prevous lecture Cocepts: t-dstrbuto, F-dstrbuto Theorems: Dstrbutos of sample mea ad sample varace, relatoshp betwee sample mea ad sample
More informationMaximum Likelihood Estimation
Marquette Uverst Maxmum Lkelhood Estmato Dael B. Rowe, Ph.D. Professor Departmet of Mathematcs, Statstcs, ad Computer Scece Coprght 08 b Marquette Uverst Maxmum Lkelhood Estmato We have bee sag that ~
More informationChapter 8. Inferences about More Than Two Population Central Values
Chapter 8. Ifereces about More Tha Two Populato Cetral Values Case tudy: Effect of Tmg of the Treatmet of Port-We tas wth Lasers ) To vestgate whether treatmet at a youg age would yeld better results tha
More informationReliability Based Design Optimization with Correlated Input Variables
7--55 Relablty Based Desg Optmzato wth Correlated Iput Varables Copyrght 7 SAE Iteratoal Kyug K. Cho, Yoojeog Noh, ad Lu Du Departmet of Mechacal & Idustral Egeerg & Ceter for Computer Aded Desg, College
More informationResearch on Moving Force Estimation of the Bridge Structure using the Adaptive Input Estimation Method
Electroc Joural of Structural Egeerg (8) 28 Research o Movg Force Estmato of the Brdge Structure usg the Adaptve Iput Estmato Method Tsug-Che Che Chug Cheg Isttute of Techology Natoal Defese Uversty Ta-Hs,
More informationMODELING AND OPTIMIZATION OF TWO-LAYER POROUS ASPHALT ROADS ABSTRACT 1- INTRODUCTION
143.DOC/1 MODELING AND OPTIMIZATION OF TWO-LAYER POROUS ASPHALT ROADS A. KUIJPERS, G. VAN BLOKLAND M+P Nose & Vbrato Cosultats, Brustesgel 3, NL-531 AD's, Hertogebosch, Netherlads Tél.: +31 73 648851 /
More informationAssignment 5/MATH 247/Winter Due: Friday, February 19 in class (!) (answers will be posted right after class)
Assgmet 5/MATH 7/Wter 00 Due: Frday, February 9 class (!) (aswers wll be posted rght after class) As usual, there are peces of text, before the questos [], [], themselves. Recall: For the quadratc form
More informationQuantitative analysis requires : sound knowledge of chemistry : possibility of interferences WHY do we need to use STATISTICS in Anal. Chem.?
Ch 4. Statstcs 4.1 Quattatve aalyss requres : soud kowledge of chemstry : possblty of terfereces WHY do we eed to use STATISTICS Aal. Chem.? ucertaty ests. wll we accept ucertaty always? f ot, from how
More informationECONOMETRIC THEORY. MODULE VIII Lecture - 26 Heteroskedasticity
ECONOMETRIC THEORY MODULE VIII Lecture - 6 Heteroskedastcty Dr. Shalabh Departmet of Mathematcs ad Statstcs Ida Isttute of Techology Kapur . Breusch Paga test Ths test ca be appled whe the replcated data
More informationBayes (Naïve or not) Classifiers: Generative Approach
Logstc regresso Bayes (Naïve or ot) Classfers: Geeratve Approach What do we mea by Geeratve approach: Lear p(y), p(x y) ad the apply bayes rule to compute p(y x) for makg predctos Ths s essetally makg
More informationC-1: Aerodynamics of Airfoils 1 C-2: Aerodynamics of Airfoils 2 C-3: Panel Methods C-4: Thin Airfoil Theory
ROAD MAP... AE301 Aerodyamcs I UNIT C: 2-D Arfols C-1: Aerodyamcs of Arfols 1 C-2: Aerodyamcs of Arfols 2 C-3: Pael Methods C-4: Th Arfol Theory AE301 Aerodyamcs I Ut C-3: Lst of Subects Problem Solutos?
More informationBayesian Inferences for Two Parameter Weibull Distribution Kipkoech W. Cheruiyot 1, Abel Ouko 2, Emily Kirimi 3
IOSR Joural of Mathematcs IOSR-JM e-issn: 78-578, p-issn: 9-765X. Volume, Issue Ver. II Ja - Feb. 05, PP 4- www.osrjourals.org Bayesa Ifereces for Two Parameter Webull Dstrbuto Kpkoech W. Cheruyot, Abel
More informationAn Introduction to. Support Vector Machine
A Itroducto to Support Vector Mache Support Vector Mache (SVM) A classfer derved from statstcal learg theory by Vapk, et al. 99 SVM became famous whe, usg mages as put, t gave accuracy comparable to eural-etwork
More informationIdea is to sample from a different distribution that picks points in important regions of the sample space. Want ( ) ( ) ( ) E f X = f x g x dx
Importace Samplg Used for a umber of purposes: Varace reducto Allows for dffcult dstrbutos to be sampled from. Sestvty aalyss Reusg samples to reduce computatoal burde. Idea s to sample from a dfferet
More informationCHAPTER VI Statistical Analysis of Experimental Data
Chapter VI Statstcal Aalyss of Expermetal Data CHAPTER VI Statstcal Aalyss of Expermetal Data Measuremets do ot lead to a uque value. Ths s a result of the multtude of errors (maly radom errors) that ca
More informationBounds on the expected entropy and KL-divergence of sampled multinomial distributions. Brandon C. Roy
Bouds o the expected etropy ad KL-dvergece of sampled multomal dstrbutos Brado C. Roy bcroy@meda.mt.edu Orgal: May 18, 2011 Revsed: Jue 6, 2011 Abstract Iformato theoretc quattes calculated from a sampled
More information: At least two means differ SST
Formula Card for Eam 3 STA33 ANOVA F-Test: Completely Radomzed Desg ( total umber of observatos, k = Number of treatmets,& T = total for treatmet ) Step : Epress the Clam Step : The ypotheses: :... 0 A
More informationChapter Statistics Background of Regression Analysis
Chapter 06.0 Statstcs Backgroud of Regresso Aalyss After readg ths chapter, you should be able to:. revew the statstcs backgroud eeded for learg regresso, ad. kow a bref hstory of regresso. Revew of Statstcal
More informationThe number of observed cases The number of parameters. ith case of the dichotomous dependent variable. the ith case of the jth parameter
LOGISTIC REGRESSION Notato Model Logstc regresso regresses a dchotomous depedet varable o a set of depedet varables. Several methods are mplemeted for selectg the depedet varables. The followg otato s
More informationEVALUATION OF FUNCTIONAL INTEGRALS BY MEANS OF A SERIES AND THE METHOD OF BOREL TRANSFORM
EVALUATION OF FUNCTIONAL INTEGRALS BY MEANS OF A SERIES AND THE METHOD OF BOREL TRANSFORM Jose Javer Garca Moreta Ph. D research studet at the UPV/EHU (Uversty of Basque coutry) Departmet of Theoretcal
More informationSolving Constrained Flow-Shop Scheduling. Problems with Three Machines
It J Cotemp Math Sceces, Vol 5, 2010, o 19, 921-929 Solvg Costraed Flow-Shop Schedulg Problems wth Three Maches P Pada ad P Rajedra Departmet of Mathematcs, School of Advaced Sceces, VIT Uversty, Vellore-632
More informationChapter 4 (Part 1): Non-Parametric Classification (Sections ) Pattern Classification 4.3) Announcements
Aoucemets No-Parametrc Desty Estmato Techques HW assged Most of ths lecture was o the blacboard. These sldes cover the same materal as preseted DHS Bometrcs CSE 90-a Lecture 7 CSE90a Fall 06 CSE90a Fall
More informationThird handout: On the Gini Index
Thrd hadout: O the dex Corrado, a tala statstca, proposed (, 9, 96) to measure absolute equalt va the mea dfferece whch s defed as ( / ) where refers to the total umber of dvduals socet. Assume that. The
More information2.28 The Wall Street Journal is probably referring to the average number of cubes used per glass measured for some population that they have chosen.
.5 x 54.5 a. x 7. 786 7 b. The raked observatos are: 7.4, 7.5, 7.7, 7.8, 7.9, 8.0, 8.. Sce the sample sze 7 s odd, the meda s the (+)/ 4 th raked observato, or meda 7.8 c. The cosumer would more lkely
More informationSimple Linear Regression and Correlation. Applied Statistics and Probability for Engineers. Chapter 11 Simple Linear Regression and Correlation
4//6 Appled Statstcs ad Probablty for Egeers Sth Edto Douglas C. Motgomery George C. Ruger Chapter Smple Lear Regresso ad Correlato CHAPTER OUTLINE Smple Lear Regresso ad Correlato - Emprcal Models -8
More informationBAYESIAN INFERENCES FOR TWO PARAMETER WEIBULL DISTRIBUTION
Iteratoal Joural of Mathematcs ad Statstcs Studes Vol.4, No.3, pp.5-39, Jue 06 Publshed by Europea Cetre for Research Trag ad Developmet UK (www.eajourals.org BAYESIAN INFERENCES FOR TWO PARAMETER WEIBULL
More informationSignal,autocorrelation -0.6
Sgal,autocorrelato Phase ose p/.9.3.7. -.5 5 5 5 Tme Sgal,autocorrelato Phase ose p/.5..7.3 -. -.5 5 5 5 Tme Sgal,autocorrelato. Phase ose p/.9.3.7. -.5 5 5 5 Tme Sgal,autocorrelato. Phase ose p/.8..6.
More informationFeature Selection: Part 2. 1 Greedy Algorithms (continued from the last lecture)
CSE 546: Mache Learg Lecture 6 Feature Selecto: Part 2 Istructor: Sham Kakade Greedy Algorthms (cotued from the last lecture) There are varety of greedy algorthms ad umerous amg covetos for these algorthms.
More informationA Robust Total Least Mean Square Algorithm For Nonlinear Adaptive Filter
A Robust otal east Mea Square Algorthm For Nolear Adaptve Flter Ruxua We School of Electroc ad Iformato Egeerg X'a Jaotog Uversty X'a 70049, P.R. Cha rxwe@chare.com Chogzhao Ha, azhe u School of Electroc
More informationA Combination of Adaptive and Line Intercept Sampling Applicable in Agricultural and Environmental Studies
ISSN 1684-8403 Joural of Statstcs Volume 15, 008, pp. 44-53 Abstract A Combato of Adaptve ad Le Itercept Samplg Applcable Agrcultural ad Evrometal Studes Azmer Kha 1 A adaptve procedure s descrbed for
More informationQuantization in Dynamic Smarandache Multi-Space
Quatzato Dyamc Smaradache Mult-Space Fu Yuhua Cha Offshore Ol Research Ceter, Beg, 7, Cha (E-mal: fuyh@cooc.com.c ) Abstract: Dscussg the applcatos of Dyamc Smaradache Mult-Space (DSMS) Theory. Supposg
More informationLogistic regression (continued)
STAT562 page 138 Logstc regresso (cotued) Suppose we ow cosder more complex models to descrbe the relatoshp betwee a categorcal respose varable (Y) that takes o two (2) possble outcomes ad a set of p explaatory
More informationChapter 11 The Analysis of Variance
Chapter The Aalyss of Varace. Oe Factor Aalyss of Varace. Radomzed Bloc Desgs (ot for ths course) NIPRL . Oe Factor Aalyss of Varace.. Oe Factor Layouts (/4) Suppose that a expermeter s terested populatos
More informationApplication of Latin Hypercube Sampling Based Kriging Surrogate Models in Reliability Assessment
Scece Joural of Appled Mathematcs ad Statstcs 5; 3(6): 63-74 Publshed ole December, 5 (http://www.scecepublshggroup.com//sams) do:.648/.sams.536.6 ISSN: 376-949 (Prt); ISSN: 376-953 (Ole) Applcato of Lat
More informationENGI 4421 Propagation of Error Page 8-01
ENGI 441 Propagato of Error Page 8-01 Propagato of Error [Navd Chapter 3; ot Devore] Ay realstc measuremet procedure cotas error. Ay calculatos based o that measuremet wll therefore also cota a error.
More informationA Multi-Entry Simulated and Inversed Function Approach. for Alternative Solutions
Iteratoal Mathematcal Forum,, 2006, o. 40, 2003 207 A Mult-Etry Smulated ad Iversed Fucto Approach for Alteratve Solutos Kev Wag a, Che Chag b ad Chug Pg Lu b a Computg ad Mathematcs School Joh Moores
More informationModel Fitting, RANSAC. Jana Kosecka
Model Fttg, RANSAC Jaa Kosecka Fttg: Issues Prevous strateges Le detecto Hough trasform Smple parametrc model, two parameters m, b m + b Votg strateg Hard to geeralze to hgher dmesos a o + a + a 2 2 +
More informationA tighter lower bound on the circuit size of the hardest Boolean functions
Electroc Colloquum o Computatoal Complexty, Report No. 86 2011) A tghter lower boud o the crcut sze of the hardest Boolea fuctos Masak Yamamoto Abstract I [IPL2005], Fradse ad Mlterse mproved bouds o the
More informationObjectives of Multiple Regression
Obectves of Multple Regresso Establsh the lear equato that best predcts values of a depedet varable Y usg more tha oe eplaator varable from a large set of potetal predctors {,,... k }. Fd that subset of
More informationResearch on SVM Prediction Model Based on Chaos Theory
Advaced Scece ad Techology Letters Vol.3 (SoftTech 06, pp.59-63 http://dx.do.org/0.457/astl.06.3.3 Research o SVM Predcto Model Based o Chaos Theory Sog Lagog, Wu Hux, Zhag Zezhog 3, College of Iformato
More informationA NEW LOG-NORMAL DISTRIBUTION
Joural of Statstcs: Advaces Theory ad Applcatos Volume 6, Number, 06, Pages 93-04 Avalable at http://scetfcadvaces.co. DOI: http://dx.do.org/0.864/jsata_700705 A NEW LOG-NORMAL DISTRIBUTION Departmet of
More informationUsing Genetic Algorithms for Solving the Comparison-Based Identification Problem of Multifactor Estimation Model
Joural of Software Egeerg ad Applcatos, 013, 6, 349-353 http://dx.do.org/10.436/sea.013.67044 Publshed Ole July 013 (http://www.scrp.org/oural/sea) 349 Usg Geetc Algorthms for Solvg the Comparso-Based
More informationEvaluation of uncertainty in measurements
Evaluato of ucertaty measuremets Laboratory of Physcs I Faculty of Physcs Warsaw Uversty of Techology Warszawa, 05 Itroducto The am of the measuremet s to determe the measured value. Thus, the measuremet
More information