Application of support vector machine in health monitoring of plate structures
|
|
- Abel Cunningham
- 5 years ago
- Views:
Transcription
1 Appcaton of support vector machne n heath montorng of pate structures *Satsh Satpa 1), Yogesh Khandare ), Sauvk Banerjee 3) and Anrban Guha 4) 1), ), 4) Department of Mechanca Engneerng, Indan Insttute of echnoogy Bombay, Mumba, Inda 3) Department of Cv Engneerng, Indan Insttute of echnoogy Bombay, Mumba, Inda 1) Satsh.satpa@gma.com ABSRAC hs paper demonstrates the use of Support Vector Machne (SVM) for detecton of damage ocaton and ts ntensty n an aumnum pate. weve damage ocatons and nne damage ntenstes have been smuated by reducng thckness of the pate at varous ocatons usng the fnte eement anayss package Abaqus. he frst mode shape data s extracted at varous ponts on the pate and t has been used as nput data for SVM to predct the damage ocatons and ther ntenstes. hs approach does not requre data of the pate n damaged state. In order to make the mode shape data more reastc n nature, Gaussan nose from 30dB to 80dB has been added. he resuts demonstrate that SVM can be used as a too for structura heath montorng wthout usng data of heathy (undamaged) state. 1. INRODUCION Structura Heath Montorng (SHM) s of great mportance n cv, mechanca and aerospace structures for safety purpose and to avod economca oss. he process of mpementng a damage dentfcaton strategy for above mentoned structures s referred to as SHM (Farrar et a., 007). he presence of damage n the structure eads to change n the moda parameters (natura frequency, dampng and stffness), and nterpretng the changes n these parameters one can ensure whether the structure s damaged or ntact. he change n the natura frequency was not suffcent to ocate the damage, hence, there was need to deveop methods based on mode shape data and Frequency Response Functon (FRF) data of the structure (Banerjee et a., 005, 009). he use of SVM for predcton of faut n power systems has been demonstrated by 1) Ph.D. Student ) P.G. Student 3) Assocate Professor 4) Assstant Professor 1631
2 Kumar et a. (011). hey used support vector cassfcaton to predct the damage ocaton. he nputs used for SVM mode are Power and Votage Vaues. Buut et a. (007) demonstrates the damage detecton n cv structure usng SVM cassfer and waveets. hey found that the SVM was a robust cassfer n presence of nose whereas waveet-based compresson gracefuy degrades ts cassfcaton accuracy. he present artce uses vbraton data (mode shape data) for regresson anayss usng SVM n order to ocate damage and ts ntensty n the rectanguar pate. Fgure 1 Damage ocatons Fgure FE mesh & data acquston ponts abe 1 modfed ocaton abes n reference to Fgure 1 Locatons from center of pate Rearranged ocaton Rada dstance (mm) Locaton abe Locaton abe Rada dstance (mm) (as per Fg. 1) (as per Fg. 1) FINIE ELEMEN MODELLING AND ANALYSIS A smpy supported pate of dmensons 500mm x 400mm x 3mm, wth foowng propertes: Young s moduus = 70GPa, Densty = 700 Kg/m3, Posson s rato = 0.3 s consdered. FE modeng and anayss of the pate s carred out n ABAQUS usng 4 163
3 node rectanguar she eement of sze 10mm X 10mm. In Fgure (1) damage ocatons are shown whch are smuated by reducng the thckness from 10% to 50 % of the orgna pate thckness n steps of 5%. However for better understandng of resuts, the pate centre s taken as reference (0, 0) and ocatons are defned as per ther rada dstance from center. he purpose of ths arrangement s to hghght trend of error n damage predcton wth respect to ocaton from the centre of the pate. he arrangement can be expaned from abe OVERVIEW OF SUPPOR VECOR MACHINE FOR REGRESSION A bref formuaton on SVM for regresson anayss gven by Vojsav (001) s presented n ths secton.svm s ntay deveoped for sovng cassfcaton probems, and successfuy apped n regresson probems. he genera formuaton of regresson earnng s carred out as foows. Gven tranng data set for earnng the machne (agorthm), t attempts to earn the nput-output reatonshp f(x). A tranng data set D = {[x (), y ()] n, = 1,, } conssts of pars (x 1, y 1 ), (x, y ),, (x, y ), where the nputs x are n- dmensona vectors x n, and the system responses y are contnuous vaues. Here frst near regresson probem formuaton s consdered and extended to non-near probem. f( x, w) w x b (1) where, x s nput vector, w s weght vector and b s bas term. ypcay regresson anayss s assocated wth approxmatng nput-output reatonshp consderng error of approxmaton. he near oss (error) functon wth nsenstvty zone ntroduced by Vapnk s gven as yf( xw, ) ε 0 y f( x, w) ε y f( x, w) ε otherwse () he near oss (error) functon wth -nsenstvty zone s shown graphcay n the Fgure (4). e Fgure 3 parameters used n (1D) SV regresson x Fgure 4 Loss (error) functon, 1633
4 he vaue gven by the Eq. (1) s predcted one and y s the actua vaue of the system response for gven nput x. he oss or error s equa to zero f the dfference between predcted and actua vaue s ess than tube. Vapnk s -nsenstvty oss functon aows us to set mt or some measure of error whch can be toerated and gven by a sma vaue. If the predcted pont es outsde the tube, then the oss s equa to magntude of the dfference between the predcted vaue and the radus of the tube whch termed as sack varabe and s gven by y f( x, w) ε ζ for data "above" an ε tube (3) y f( x, w) ε ζ * for data "beow" an ε tube (4) as A new emprca rsk s ntroduced n order to perform SVM regresson and s gven R ε emp 1 wb, yw xb 1 ε (5) he objectve of SVM regresson s to mnmze the emprca rsk R ε emp and norm of w wegh vector smutaneousy. hus, man goa s to estmate a near regresson hyperpane f( x, w) w xb by mnmzng 1 R w C yw xb (6) 1 ε Usng expressons for sack varabes the emprca rsk becomes Under the constrants 1 R w C ζ ζ * (7) 1 1 y w x b ε ζ, 1 * w x b y ε ζ, 1 ζ 0, 1 ζ * 0, 1 (8) (9) here are many two parameters whch have to be tuned to get good performance from SVM regresson anayss. he constant C nfuences the trade-off between an approxmaton error and the weght vector norm. Another parameter whch has to choose by the user, that defnes the precson requred n predcton. hs constraned probem s soved by formng prma Lagrangan (L p ) functon, and s gven by 1634
5 * * * 1 * * * * wbζ,,, ζ α, α, β, β w C ζ ζ α y x b ε ζ βζ βζ Lp w w (10) hs prma Lagrangan functon has to be mnmzed wth respect to prma varabes w, b,, and and maxmzed wth respect to,,,. he probem s soved n ts dua form and s gven as foows, Maxmze Subject to * * * 1 * * Ld α, α εα αα αy α α α j α jx x j (11) 1 1, j1 * α α (1) 1 1 * 0 α C, 1 0 α C, 1 (13) If we ook at the dua form of probem t s expressed n terms of Lagrange mutpers and ony. hs standard optmzaton probem can be expressed n a matrx form and gven as: Mnmze Subject to constrants Eqs. (1), (13). Where for near regresson α L 0.5 d α Hα f (14) H x x1 (15) f εy εy εy εy εy εy (16) 1 N 1 he souton of above probem w gve Lagrange mutpers pars. he number of support vector s equa to the nonzero parameters or. After cacuatng Lagrange mutpers the weght vector and bas term s found as foows * 1 w α α x (17) N 1 y x 1 b w (18) he best regresson hyperpane n case of near probem s gven by f( x, w) w x b (19) 1635
6 Whe desgnng SV machnes for non-near regresson anayss frst map the nput vectors x n n to vectors z of a hgher-dmensona feature space F, where ϕ represents a mappng), and sove a near regresson probem n ths feature space. he most mappng (kerne) functons are poynomas and rada bass functons wth Gaussan kernes. he gven optmzaton probem s soved wth change n ony Hessan matrx H and s gven as H G G G G (0) Where G s the correspondng kerne matrx G (, ) and weght vector and bas term s gven by w α * α (1) 1 b y g 1 () and the best non-near regresson functon s gven by g Gw (3) z f x, w Gw b (4) 4. RESULS AND DISCUSSION Snce SVM regresson agorthm gves ony snge output, SVM regresson anayss s carred out n two stages. 4.1 SAGE1: DAMAGE LOCAION PREDICION he damage ocaton predcton was done n two steps. Step 1 nvoved predctng the X coordnate and step nvoved predctng the Y coordnate of the damage ocaton. he tranng nput set used for step 1 s mode shape data for a damage ntenstes and tranng output set was correspondng X coordnate of damage ocatons. est set was the mode shape data whose damage ocaton and ntensty was to be predcted. SVM now predcts X coordnate of damage ocaton n step 1. Step was smar to step one except that the Y coordnate of damage ocaton was predcted. Stage nvoved damage ntensty predcton. In ths stage, mode shape data for a partcuar ocaton was used as nput and damage ntensty at that ocaton was used as output. hs was repeated for a the ocatons. Parameters for SVR are taken as: C=, e=0.0005, Rada Bass functon (RBF) kerne, - nsenstve oss functon, kerne wdth=0.6 for damage ocaton predcton, and C=10, kerne wdth=1 for damage ntensty. he percentage error s cacuated as gven beow. 1636
7 X X Y Y % error maxmum ength of dagona X 100 (1) Frst mode shape data obtaned at a the ponts of the smuated rectanguar pate hghghted n the Fgure s consdered as tranng nput for the SVM, and correspondng damage ocaton and/or ntensty as tranng output. he damage ocaton s represented by the mdpont of the damaged area n order to get snge vaued output for the SVM. abe Error n damage ocaton predcton averaged over damage ocaton of pate nose eve Intensty% no nose 80 db 70dB 60 db 50 db 40 db 30 db % Error no nose 80 db 70dB 60 db 50 db 40 db 30 db % Error no nose 80 db 70 db 60 db 50 db 40 db 30 db Damage ntenstes % Damage ocaton Fgure 5 Error n damage ocaton predcton averaged over damage ntenstes Fgure 6 Error n damage ocaton predcton averaged over damage ocaton he same % errors for consdered nose eve cases now are averaged over damage ntensty and the varaton of % error wth the damage ocatons s tabuated n tabe 3 and s potted n the Fgure 5 averaged over damage ntenstes and averaged over damage ocatons n Fgure 6 respectvey. For no nose case, the % error remans beow % up to damage ocaton 134mm and t suddeny ncreases at the ocatons 1637
8 14mm and 156mm whch are far away from the center of the pate. As we add nose n the data for ow nose eves the same error, whch was up to 134mm n the case of no nose case, now t s at 15mm. he detaed resuts are gven n the tabe. abe 3 Error n damage ocaton predcton averaged over damage ntensty of pate Dstance nose (mm) no nose db db db db db db SAGE: DAMAGE INENSIY PREDICION abe 3 summarzes the error n ntensty predcton by SVM for those ocatons found n the stage 1. For nose eve up to 50dB the % errors are amost same at ow damage ntensty. abe 3 Error n damage ntensty predcton averaged over damage ocaton of pate nose no nose Intensty% 80 db 70dB 60 db 50 db 40 db 30 db he percentage error n ntensty predcton s cacuated as gven beow % error Damage ntensty Damage ntensty Damage ntensty X 100 () 1638
9 % Error no nose 80 db 70 db 60 db 50 db 40 db 30 db Damage ocaton Fgure 7 Error n damage ntensty predcton averaged over damage ocaton for ow nose eve % Error no nose 80 db 70dB 60 db 50 db 40 db 30 db Damage ntenstes n % Fgure 8 Error n damage ntensty predcton averaged over damage ocaton for hgh nose eve abe 4 represents the detaed vaues of % error for dfferent nose eves ncudng no nose case, and t s potted n the Fgure 7 and Fgure 8. For no nose case the % error s hgh for ony two ocatons (14mm and 156mm) but, when we add the nose, t s hgh for three ocatons for nose eves 80dB to 50dB. he error for the case of 40dB nose s acceptabe ony for the ocatons coser to the center of the pate.e. up to 75mm from the center. abe 4 Error n damage ntensty predcton averaged over damage ntensty of pate Dstance nose no nose db db db db db db CONCLUSIONS he SVM has been traned wth vbraton-nduced dspacements coected at 99 ponts for the frst mode shape as nput and damage ntensty or ocaton as output. After tranng, the SVM s abe to predct any damage ntensty or ocaton of the tranng set data wth amost neggbe error. he % error n predcton of damage ocaton and ntensty s ess at the center of the pate and goes on ncreasng away from the center. he predcton capabty of SVM s degraded wth addton of nose n the data. For ow 1639
10 nose eves % error remans amost same as that of no nose case n the data that means SVM can toerate such nose eves wth ess devaton n the errors. REFERENCES Banerjee S, Rcc F, Monaco E, Ma A (009), A wave propagaton and vbraton based approach for damage dentfcaton n structura components. Journa of Sound and Vbraton (3), Buut A, Sng A.K, Shn P, Fountan, Jasso H, Yan L, Egama A (005), Rea-tmenon destructve structura heath montorng usng support vector machnes and waveets. In: SPIE 5770, Advanced Sensor echnooges for Nondestructve Evauaton and Structura Heath Montorng, 180. UC Santa Barbara, Santa Barbara, 13 May 005. Cherkassky V, Ma V (004), Practca seecton of SVM parameters and nose estmaton for SVM regresson.neura Network (17), Farrar CR, Worden K (007), An ntroducton to structura heath montorng. Ph rans R Soc A (365), Kumar SK, Jayabarath, Naveen S (011), Faut dentfcaton and ocaton n dstrbuton systems usng support vector machnes. European Journa Scentfc Research (51), Lee Jong Won, Krkera Goutham. R, Kang Inp, Schuz Mark J and Shanov Vessen.N (006), Structura heath montorng usng contnuous sensors and neura network anayss, Smart Mater.Struct. (15), Ma A, Rcc F, Banerjee S, Shh F (005), A conceptua structura heath montorng system based on vbraton and wave propagaton. Structura Heath Montorng 4(3),
Neural network-based athletics performance prediction optimization model applied research
Avaabe onne www.jocpr.com Journa of Chemca and Pharmaceutca Research, 04, 6(6):8-5 Research Artce ISSN : 0975-784 CODEN(USA) : JCPRC5 Neura networ-based athetcs performance predcton optmzaton mode apped
More informationExample: Suppose we want to build a classifier that recognizes WebPages of graduate students.
Exampe: Suppose we want to bud a cassfer that recognzes WebPages of graduate students. How can we fnd tranng data? We can browse the web and coect a sampe of WebPages of graduate students of varous unverstes.
More informationImage Classification Using EM And JE algorithms
Machne earnng project report Fa, 2 Xaojn Sh, jennfer@soe Image Cassfcaton Usng EM And JE agorthms Xaojn Sh Department of Computer Engneerng, Unversty of Caforna, Santa Cruz, CA, 9564 jennfer@soe.ucsc.edu
More informationDeriving the Dual. Prof. Bennett Math of Data Science 1/13/06
Dervng the Dua Prof. Bennett Math of Data Scence /3/06 Outne Ntty Grtty for SVM Revew Rdge Regresson LS-SVM=KRR Dua Dervaton Bas Issue Summary Ntty Grtty Need Dua of w, b, z w 2 2 mn st. ( x w ) = C z
More informationNONLINEAR SYSTEM IDENTIFICATION BASE ON FW-LSSVM
Journa of heoretca and Apped Informaton echnoogy th February 3. Vo. 48 No. 5-3 JAI & LLS. A rghts reserved. ISSN: 99-8645 www.jatt.org E-ISSN: 87-395 NONLINEAR SYSEM IDENIFICAION BASE ON FW-LSSVM, XIANFANG
More informationSupport Vector Machines. Vibhav Gogate The University of Texas at dallas
Support Vector Machnes Vbhav Gogate he Unversty of exas at dallas What We have Learned So Far? 1. Decson rees. Naïve Bayes 3. Lnear Regresson 4. Logstc Regresson 5. Perceptron 6. Neural networks 7. K-Nearest
More informationSupport Vector Machines
Separatng boundary, defned by w Support Vector Machnes CISC 5800 Professor Danel Leeds Separatng hyperplane splts class 0 and class 1 Plane s defned by lne w perpendcular to plan Is data pont x n class
More informationResearch on Complex Networks Control Based on Fuzzy Integral Sliding Theory
Advanced Scence and Technoogy Letters Vo.83 (ISA 205), pp.60-65 http://dx.do.org/0.4257/ast.205.83.2 Research on Compex etworks Contro Based on Fuzzy Integra Sdng Theory Dongsheng Yang, Bngqng L, 2, He
More informationReactive Power Allocation Using Support Vector Machine
Reactve Power Aocaton Usng Support Vector Machne M.W. Mustafa, S.N. Khad, A. Kharuddn Facuty of Eectrca Engneerng, Unverst Teknoog Maaysa Johor 830, Maaysa and H. Shareef Facuty of Eectrca Engneerng and
More informationShort-Term Load Forecasting for Electric Power Systems Using the PSO-SVR and FCM Clustering Techniques
Energes 20, 4, 73-84; do:0.3390/en40073 Artce OPEN ACCESS energes ISSN 996-073 www.mdp.com/journa/energes Short-Term Load Forecastng for Eectrc Power Systems Usng the PSO-SVR and FCM Custerng Technques
More informationWAVELET-BASED IMAGE COMPRESSION USING SUPPORT VECTOR MACHINE LEARNING AND ENCODING TECHNIQUES
WAVELE-BASED IMAGE COMPRESSION USING SUPPOR VECOR MACHINE LEARNING AND ENCODING ECHNIQUES Rakb Ahmed Gppsand Schoo of Computng and Informaton echnoogy Monash Unversty, Gppsand Campus Austraa. Rakb.Ahmed@nfotech.monash.edu.au
More informationThe University of Auckland, School of Engineering SCHOOL OF ENGINEERING REPORT 616 SUPPORT VECTOR MACHINES BASICS. written by.
The Unversty of Auckand, Schoo of Engneerng SCHOOL OF ENGINEERING REPORT 66 SUPPORT VECTOR MACHINES BASICS wrtten by Vojsav Kecman Schoo of Engneerng The Unversty of Auckand Apr, 004 Vojsav Kecman Copyrght,
More informationLecture Notes on Linear Regression
Lecture Notes on Lnear Regresson Feng L fl@sdueducn Shandong Unversty, Chna Lnear Regresson Problem In regresson problem, we am at predct a contnuous target value gven an nput feature vector We assume
More informationLinear Classification, SVMs and Nearest Neighbors
1 CSE 473 Lecture 25 (Chapter 18) Lnear Classfcaton, SVMs and Nearest Neghbors CSE AI faculty + Chrs Bshop, Dan Klen, Stuart Russell, Andrew Moore Motvaton: Face Detecton How do we buld a classfer to dstngush
More informationSupport Vector Machines
/14/018 Separatng boundary, defned by w Support Vector Machnes CISC 5800 Professor Danel Leeds Separatng hyperplane splts class 0 and class 1 Plane s defned by lne w perpendcular to plan Is data pont x
More informationADVANCED MACHINE LEARNING ADVANCED MACHINE LEARNING
1 ADVANCED ACHINE LEARNING ADVANCED ACHINE LEARNING Non-lnear regresson technques 2 ADVANCED ACHINE LEARNING Regresson: Prncple N ap N-dm. nput x to a contnuous output y. Learn a functon of the type: N
More informationAssociative Memories
Assocatve Memores We consder now modes for unsupervsed earnng probems, caed auto-assocaton probems. Assocaton s the task of mappng patterns to patterns. In an assocatve memory the stmuus of an ncompete
More informationIDENTIFICATION OF NONLINEAR SYSTEM VIA SVR OPTIMIZED BY PARTICLE SWARM ALGORITHM
Journa of Theoretca and Apped Informaton Technoogy th February 3. Vo. 48 No. 5-3 JATIT & LLS. A rghts reserved. ISSN: 99-8645 www.att.org E-ISSN: 87-395 IDENTIFICATION OF NONLINEAR SYSTEM VIA SVR OPTIMIZED
More informationKernel Methods and SVMs Extension
Kernel Methods and SVMs Extenson The purpose of ths document s to revew materal covered n Machne Learnng 1 Supervsed Learnng regardng support vector machnes (SVMs). Ths document also provdes a general
More informationOn the Equality of Kernel AdaTron and Sequential Minimal Optimization in Classification and Regression Tasks and Alike Algorithms for Kernel
Proceedngs of th European Symposum on Artfca Neura Networks, pp. 25-222, ESANN 2003, Bruges, Begum, 2003 On the Equaty of Kerne AdaTron and Sequenta Mnma Optmzaton n Cassfcaton and Regresson Tasks and
More informationWhich Separator? Spring 1
Whch Separator? 6.034 - Sprng 1 Whch Separator? Mamze the margn to closest ponts 6.034 - Sprng Whch Separator? Mamze the margn to closest ponts 6.034 - Sprng 3 Margn of a pont " # y (w $ + b) proportonal
More informationMACHINE APPLIED MACHINE LEARNING LEARNING. Gaussian Mixture Regression
11 MACHINE APPLIED MACHINE LEARNING LEARNING MACHINE LEARNING Gaussan Mture Regresson 22 MACHINE APPLIED MACHINE LEARNING LEARNING Bref summary of last week s lecture 33 MACHINE APPLIED MACHINE LEARNING
More informationA finite difference method for heat equation in the unbounded domain
Internatona Conerence on Advanced ectronc Scence and Technoogy (AST 6) A nte derence method or heat equaton n the unbounded doman a Quan Zheng and Xn Zhao Coege o Scence North Chna nversty o Technoogy
More informationREAL-TIME IMPACT FORCE IDENTIFICATION OF CFRP LAMINATED PLATES USING SOUND WAVES
8 TH INTERNATIONAL CONERENCE ON COMPOSITE MATERIALS REAL-TIME IMPACT ORCE IDENTIICATION O CRP LAMINATED PLATES USING SOUND WAVES S. Atobe *, H. Kobayash, N. Hu 3 and H. ukunaga Department of Aerospace
More informationSupport Vector Machine Technique for Wind Speed Prediction
Internatona Proceedngs of Chemca, Boogca and Envronmenta Engneerng, Vo. 93 (016) DOI: 10.7763/IPCBEE. 016. V93. Support Vector Machne Technque for Wnd Speed Predcton Yusuf S. Turkan 1 and Hacer Yumurtacı
More informationERROR MODELING FOR STRUCTURAL DEFORMATIONS OF MULTI-AXIS SYSTEM BASED ON SVR
Journa of Theoretca and Apped Informaton Technoogy 3 st January 03. Vo. 47 No.3 005-03 JATIT & LLS. A rghts reserved. ISSN: 99-8645 www.jatt.org E-ISSN: 87-395 ERROR MODELING FOR STRUCTURAL DEFORMATIONS
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
More informationA DIMENSION-REDUCTION METHOD FOR STOCHASTIC ANALYSIS SECOND-MOMENT ANALYSIS
A DIMESIO-REDUCTIO METHOD FOR STOCHASTIC AALYSIS SECOD-MOMET AALYSIS S. Rahman Department of Mechanca Engneerng and Center for Computer-Aded Desgn The Unversty of Iowa Iowa Cty, IA 52245 June 2003 OUTLIE
More informationNatural Language Processing and Information Retrieval
Natural Language Processng and Informaton Retreval Support Vector Machnes Alessandro Moschtt Department of nformaton and communcaton technology Unversty of Trento Emal: moschtt@ds.untn.t Summary Support
More informationStrain Energy in Linear Elastic Solids
Duke Unverst Department of Cv and Envronmenta Engneerng CEE 41L. Matr Structura Anass Fa, Henr P. Gavn Stran Energ n Lnear Eastc Sods Consder a force, F, apped gradua to a structure. Let D be the resutng
More information3. Stress-strain relationships of a composite layer
OM PO I O U P U N I V I Y O F W N ompostes ourse 8-9 Unversty of wente ng. &ech... tress-stran reatonshps of a composte ayer - Laurent Warnet & emo Aerman.. tress-stran reatonshps of a composte ayer Introducton
More informationCOXREG. Estimation (1)
COXREG Cox (972) frst suggested the modes n whch factors reated to fetme have a mutpcatve effect on the hazard functon. These modes are caed proportona hazards (PH) modes. Under the proportona hazards
More informationLower Bounding Procedures for the Single Allocation Hub Location Problem
Lower Boundng Procedures for the Snge Aocaton Hub Locaton Probem Borzou Rostam 1,2 Chrstoph Buchhem 1,4 Fautät für Mathemat, TU Dortmund, Germany J. Faban Meer 1,3 Uwe Causen 1 Insttute of Transport Logstcs,
More informationLINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity
LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 30 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 2 Remedes for multcollnearty Varous technques have
More informationOptimum Selection Combining for M-QAM on Fading Channels
Optmum Seecton Combnng for M-QAM on Fadng Channes M. Surendra Raju, Ramesh Annavajjaa and A. Chockangam Insca Semconductors Inda Pvt. Ltd, Bangaore-56000, Inda Department of ECE, Unversty of Caforna, San
More informationSparse Training Procedure for Kernel Neuron *
Sparse ranng Procedure for Kerne Neuron * Janhua XU, Xuegong ZHANG and Yanda LI Schoo of Mathematca and Computer Scence, Nanng Norma Unversty, Nanng 0097, Jangsu Provnce, Chna xuanhua@ema.nnu.edu.cn Department
More informationSupporting Information
Supportng Informaton The neural network f n Eq. 1 s gven by: f x l = ReLU W atom x l + b atom, 2 where ReLU s the element-wse rectfed lnear unt, 21.e., ReLUx = max0, x, W atom R d d s the weght matrx to
More informationLINEAR REGRESSION ANALYSIS. MODULE IX Lecture Multicollinearity
LINEAR REGRESSION ANALYSIS MODULE IX Lecture - 31 Multcollnearty Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur 6. Rdge regresson The OLSE s the best lnear unbased
More informationOn the Power Function of the Likelihood Ratio Test for MANOVA
Journa of Mutvarate Anayss 8, 416 41 (00) do:10.1006/jmva.001.036 On the Power Functon of the Lkehood Rato Test for MANOVA Dua Kumar Bhaumk Unversty of South Aabama and Unversty of Inos at Chcago and Sanat
More informationNested case-control and case-cohort studies
Outne: Nested case-contro and case-cohort studes Ørnuf Borgan Department of Mathematcs Unversty of Oso NORBIS course Unversty of Oso 4-8 December 217 1 Radaton and breast cancer data Nested case contro
More informationSupplementary Material: Learning Structured Weight Uncertainty in Bayesian Neural Networks
Shengyang Sun, Changyou Chen, Lawrence Carn Suppementary Matera: Learnng Structured Weght Uncertanty n Bayesan Neura Networks Shengyang Sun Changyou Chen Lawrence Carn Tsnghua Unversty Duke Unversty Duke
More informationSupervised Learning. Neural Networks and Back-Propagation Learning. Credit Assignment Problem. Feedforward Network. Adaptive System.
Part 7: Neura Networ & earnng /2/05 Superved earnng Neura Networ and Bac-Propagaton earnng Produce dered output for tranng nput Generaze reaonaby & appropratey to other nput Good exampe: pattern recognton
More informationInductance Calculation for Conductors of Arbitrary Shape
CRYO/02/028 Aprl 5, 2002 Inductance Calculaton for Conductors of Arbtrary Shape L. Bottura Dstrbuton: Internal Summary In ths note we descrbe a method for the numercal calculaton of nductances among conductors
More informationXin Li Department of Information Systems, College of Business, City University of Hong Kong, Hong Kong, CHINA
RESEARCH ARTICLE MOELING FIXE OS BETTING FOR FUTURE EVENT PREICTION Weyun Chen eartment of Educatona Informaton Technoogy, Facuty of Educaton, East Chna Norma Unversty, Shangha, CHINA {weyun.chen@qq.com}
More informationModule 3: Element Properties Lecture 1: Natural Coordinates
Module 3: Element Propertes Lecture : Natural Coordnates Natural coordnate system s bascally a local coordnate system whch allows the specfcaton of a pont wthn the element by a set of dmensonless numbers
More informationOne-sided finite-difference approximations suitable for use with Richardson extrapolation
Journal of Computatonal Physcs 219 (2006) 13 20 Short note One-sded fnte-dfference approxmatons sutable for use wth Rchardson extrapolaton Kumar Rahul, S.N. Bhattacharyya * Department of Mechancal Engneerng,
More informationNUMERICAL DIFFERENTIATION
NUMERICAL DIFFERENTIATION 1 Introducton Dfferentaton s a method to compute the rate at whch a dependent output y changes wth respect to the change n the ndependent nput x. Ths rate of change s called the
More informationNon-linear Canonical Correlation Analysis Using a RBF Network
ESANN' proceedngs - European Smposum on Artfcal Neural Networks Bruges (Belgum), 4-6 Aprl, d-sde publ., ISBN -97--, pp. 57-5 Non-lnear Canoncal Correlaton Analss Usng a RBF Network Sukhbnder Kumar, Elane
More informationThe Application of BP Neural Network principal component analysis in the Forecasting the Road Traffic Accident
ICTCT Extra Workshop, Bejng Proceedngs The Appcaton of BP Neura Network prncpa component anayss n Forecastng Road Traffc Accdent He Mng, GuoXucheng &LuGuangmng Transportaton Coege of Souast Unversty 07
More informationwe have E Y x t ( ( xl)) 1 ( xl), e a in I( Λ ) are as follows:
APPENDICES Aendx : the roof of Equaton (6 For j m n we have Smary from Equaton ( note that j '( ( ( j E Y x t ( ( x ( x a V ( ( x a ( ( x ( x b V ( ( x b V x e d ( abx ( ( x e a a bx ( x xe b a bx By usng
More informationMultispectral Remote Sensing Image Classification Algorithm Based on Rough Set Theory
Proceedngs of the 2009 IEEE Internatona Conference on Systems Man and Cybernetcs San Antono TX USA - October 2009 Mutspectra Remote Sensng Image Cassfcaton Agorthm Based on Rough Set Theory Yng Wang Xaoyun
More informationLecture 10 Support Vector Machines. Oct
Lecture 10 Support Vector Machnes Oct - 20-2008 Lnear Separators Whch of the lnear separators s optmal? Concept of Margn Recall that n Perceptron, we learned that the convergence rate of the Perceptron
More informationCS 3710: Visual Recognition Classification and Detection. Adriana Kovashka Department of Computer Science January 13, 2015
CS 3710: Vsual Recognton Classfcaton and Detecton Adrana Kovashka Department of Computer Scence January 13, 2015 Plan for Today Vsual recognton bascs part 2: Classfcaton and detecton Adrana s research
More information10-701/ Machine Learning, Fall 2005 Homework 3
10-701/15-781 Machne Learnng, Fall 2005 Homework 3 Out: 10/20/05 Due: begnnng of the class 11/01/05 Instructons Contact questons-10701@autonlaborg for queston Problem 1 Regresson and Cross-valdaton [40
More informationCyclic Codes BCH Codes
Cycc Codes BCH Codes Gaos Feds GF m A Gaos fed of m eements can be obtaned usng the symbos 0,, á, and the eements beng 0,, á, á, á 3 m,... so that fed F* s cosed under mutpcaton wth m eements. The operator
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 informationOptimization of JK Flip Flop Layout with Minimal Average Power of Consumption based on ACOR, Fuzzy-ACOR, GA, and Fuzzy-GA
Journa of mathematcs and computer Scence 4 (05) - 5 Optmzaton of JK Fp Fop Layout wth Mnma Average Power of Consumpton based on ACOR, Fuzzy-ACOR, GA, and Fuzzy-GA Farshd Kevanan *,, A Yekta *,, Nasser
More informationA New Modified Gaussian Mixture Model for Color-Texture Segmentation
Journa of Computer Scence 7 (): 79-83, 0 ISSN 549-3636 0 Scence Pubcatons A New Modfed Gaussan Mxture Mode for Coor-Texture Segmentaton M. Sujartha and S. Annadura Department of Computer Scence and Engneerng,
More informationThe Entire Solution Path for Support Vector Machine in Positive and Unlabeled Classification 1
Abstract The Entre Souton Path for Support Vector Machne n Postve and Unabeed Cassfcaton 1 Yao Lmn, Tang Je, and L Juanz Department of Computer Scence, Tsnghua Unversty 1-308, FIT, Tsnghua Unversty, Bejng,
More informationA Three-Phase State Estimation in Unbalanced Distribution Networks with Switch Modelling
A Three-Phase State Estmaton n Unbaanced Dstrbuton Networks wth Swtch Modeng Ankur Majumdar Student Member, IEEE Dept of Eectrca and Eectronc Engneerng Impera Coege London London, UK ankurmajumdar@mperaacuk
More informationSolutions to exam in SF1811 Optimization, Jan 14, 2015
Solutons to exam n SF8 Optmzaton, Jan 4, 25 3 3 O------O -4 \ / \ / The network: \/ where all lnks go from left to rght. /\ / \ / \ 6 O------O -5 2 4.(a) Let x = ( x 3, x 4, x 23, x 24 ) T, where the varable
More informationChapter 6 Support vector machine. Séparateurs à vaste marge
Chapter 6 Support vector machne Séparateurs à vaste marge Méthode de classfcaton bnare par apprentssage Introdute par Vladmr Vapnk en 1995 Repose sur l exstence d un classfcateur lnéare Apprentssage supervsé
More informationComposite Hypotheses testing
Composte ypotheses testng In many hypothess testng problems there are many possble dstrbutons that can occur under each of the hypotheses. The output of the source s a set of parameters (ponts n a parameter
More informationJournal of Multivariate Analysis
Journa of Mutvarate Anayss 3 (04) 74 96 Contents sts avaabe at ScenceDrect Journa of Mutvarate Anayss journa homepage: www.esever.com/ocate/jmva Hgh-dmensona sparse MANOVA T. Tony Ca a, Yn Xa b, a Department
More informationCluster Validation Determining Number of Clusters. Umut ORHAN, PhD.
Cluster Analyss Cluster Valdaton Determnng Number of Clusters 1 Cluster Valdaton The procedure of evaluatng the results of a clusterng algorthm s known under the term cluster valdty. How do we evaluate
More informationLecture 3: Dual problems and Kernels
Lecture 3: Dual problems and Kernels C4B Machne Learnng Hlary 211 A. Zsserman Prmal and dual forms Lnear separablty revsted Feature mappng Kernels for SVMs Kernel trck requrements radal bass functons SVM
More informationActive Learning with Support Vector Machines for Tornado Prediction
Actve Learnng wth Support Vector Machnes for Tornado Predcton Theodore B. Trafas, Indra Adranto, and Mchae B. Rchman Schoo of Industra Engneerng, Unversty of Okahoma, 0 West Boyd St, Room 4, Norman, OK
More informationMore metrics on cartesian products
More metrcs on cartesan products If (X, d ) are metrc spaces for 1 n, then n Secton II4 of the lecture notes we defned three metrcs on X whose underlyng topologes are the product topology The purpose of
More informationQUARTERLY OF APPLIED MATHEMATICS
QUARTERLY OF APPLIED MATHEMATICS Voume XLI October 983 Number 3 DIAKOPTICS OR TEARING-A MATHEMATICAL APPROACH* By P. W. AITCHISON Unversty of Mantoba Abstract. The method of dakoptcs or tearng was ntroduced
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 informationAnalysis of CMPP Approach in Modeling Broadband Traffic
Anayss of Approach n Modeng Broadband Traffc R.G. Garroppo, S. Gordano, S. Lucett, and M. Pagano Department of Informaton Engneerng, Unversty of Psa Va Dotsav - 566 Psa - Itay {r.garroppo, s.gordano, s.ucett,
More informationRichard Socher, Henning Peters Elements of Statistical Learning I E[X] = arg min. E[(X b) 2 ]
1 Prolem (10P) Show that f X s a random varale, then E[X] = arg mn E[(X ) 2 ] Thus a good predcton for X s E[X] f the squared dfference s used as the metrc. The followng rules are used n the proof: 1.
More informationGENERATIVE AND DISCRIMINATIVE CLASSIFIERS: NAIVE BAYES AND LOGISTIC REGRESSION. Machine Learning
CHAPTER 3 GENERATIVE AND DISCRIMINATIVE CLASSIFIERS: NAIVE BAYES AND LOGISTIC REGRESSION Machne Learnng Copyrght c 205. Tom M. Mtche. A rghts reserved. *DRAFT OF September 23, 207* *PLEASE DO NOT DISTRIBUTE
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Exerments-I MODULE III LECTURE - 2 EXPERIMENTAL DESIGN MODELS Dr. Shalabh Deartment of Mathematcs and Statstcs Indan Insttute of Technology Kanur 2 We consder the models
More informationLower bounds for the Crossing Number of the Cartesian Product of a Vertex-transitive Graph with a Cycle
Lower bounds for the Crossng Number of the Cartesan Product of a Vertex-transtve Graph wth a Cyce Junho Won MIT-PRIMES December 4, 013 Abstract. The mnmum number of crossngs for a drawngs of a gven graph
More informationA General Column Generation Algorithm Applied to System Reliability Optimization Problems
A Genera Coumn Generaton Agorthm Apped to System Reabty Optmzaton Probems Lea Za, Davd W. Cot, Department of Industra and Systems Engneerng, Rutgers Unversty, Pscataway, J 08854, USA Abstract A genera
More informationSampling-based Approach for Design Optimization in the Presence of Interval Variables
0 th Word Congress on Structura and Mutdscpnary Optmzaton May 9-4, 03, Orando, orda, USA Sampng-based Approach for Desgn Optmzaton n the Presence of nterva Varabes Davd Yoo and kn Lee Unversty of Connectcut,
More informationChapter 6. Rotations and Tensors
Vector Spaces n Physcs 8/6/5 Chapter 6. Rotatons and ensors here s a speca knd of near transformaton whch s used to transforms coordnates from one set of axes to another set of axes (wth the same orgn).
More information1 Convex Optimization
Convex Optmzaton We wll consder convex optmzaton problems. Namely, mnmzaton problems where the objectve s convex (we assume no constrants for now). Such problems often arse n machne learnng. For example,
More informationLecture 6: Introduction to Linear Regression
Lecture 6: Introducton to Lnear Regresson An Manchakul amancha@jhsph.edu 24 Aprl 27 Lnear regresson: man dea Lnear regresson can be used to study an outcome as a lnear functon of a predctor Example: 6
More informationSupport Vector Machines for Classification and Regression
ISIS Technca Report Support Vector Machnes for Cassfcaton and Regresson Steve Gunn 0 November 997 Contents Introducton 3 2 Support Vector Cassfcaton 4 2. The Optma Separatng Hyperpane...5 2.. Lneary Separabe
More informationPart II. Support Vector Machines
Part II Support Vector Machnes 35 Chapter 5 Lnear Cassfcaton 5. Lnear Cassfers on Lnear Separabe Data As a frst step n understandng and constructng Support Vector Machnes e stud the case of near separabe
More informationProblem Set 9 Solutions
Desgn and Analyss of Algorthms May 4, 2015 Massachusetts Insttute of Technology 6.046J/18.410J Profs. Erk Demane, Srn Devadas, and Nancy Lynch Problem Set 9 Solutons Problem Set 9 Solutons Ths problem
More informationThe Geometry of Logit and Probit
The Geometry of Logt and Probt Ths short note s meant as a supplement to Chapters and 3 of Spatal Models of Parlamentary Votng and the notaton and reference to fgures n the text below s to those two chapters.
More informationON AUTOMATIC CONTINUITY OF DERIVATIONS FOR BANACH ALGEBRAS WITH INVOLUTION
European Journa of Mathematcs and Computer Scence Vo. No. 1, 2017 ON AUTOMATC CONTNUTY OF DERVATONS FOR BANACH ALGEBRAS WTH NVOLUTON Mohamed BELAM & Youssef T DL MATC Laboratory Hassan Unversty MORO CCO
More informationDynamic Analysis Of An Off-Road Vehicle Frame
Proceedngs of the 8th WSEAS Int. Conf. on NON-LINEAR ANALYSIS, NON-LINEAR SYSTEMS AND CHAOS Dnamc Anass Of An Off-Road Vehce Frame ŞTEFAN TABACU, NICOLAE DORU STĂNESCU, ION TABACU Automotve Department,
More informationThe Concept of Beamforming
ELG513 Smart Antennas S.Loyka he Concept of Beamformng Generc representaton of the array output sgnal, 1 where w y N 1 * = 1 = w x = w x (4.1) complex weghts, control the array pattern; y and x - narrowband
More informationACCURATE COMPUTATION OF CRITICAL RESPONSE QUANTITES FOR LAMINATED COMPOSITE STRUCTURES
ACCURATE COMPUTATION OF CRITICAL RESPONSE QUANTITES FOR LAMINATED COMPOSITE STRUCTURES C.S. UPADHYAY, P.M. MOHITE and A. K. ONKAR Department of Aerospace Engneerng Indan Insttute of Technoogy Kanpur Kanpur
More informationChapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems
Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons
More informationCharacterizing Probability-based Uniform Sampling for Surrogate Modeling
th Word Congress on Structura and Mutdscpnary Optmzaton May 9-4, 3, Orando, Forda, USA Characterzng Probabty-based Unform Sampng for Surrogate Modeng Junqang Zhang, Souma Chowdhury, Ache Messac 3 Syracuse
More informationLinear Approximation with Regularization and Moving Least Squares
Lnear Approxmaton wth Regularzaton and Movng Least Squares Igor Grešovn May 007 Revson 4.6 (Revson : March 004). 5 4 3 0.5 3 3.5 4 Contents: Lnear Fttng...4. Weghted Least Squares n Functon Approxmaton...
More informationAn identification algorithm of model kinetic parameters of the interfacial layer growth in fiber composites
IOP Conference Seres: Materals Scence and Engneerng PAPER OPE ACCESS An dentfcaton algorthm of model knetc parameters of the nterfacal layer growth n fber compostes o cte ths artcle: V Zubov et al 216
More informationFinite Element Modelling of truss/cable structures
Pet Schreurs Endhoven Unversty of echnology Department of Mechancal Engneerng Materals echnology November 3, 214 Fnte Element Modellng of truss/cable structures 1 Fnte Element Analyss of prestressed structures
More informationPulse Coded Modulation
Pulse Coded Modulaton PCM (Pulse Coded Modulaton) s a voce codng technque defned by the ITU-T G.711 standard and t s used n dgtal telephony to encode the voce sgnal. The frst step n the analog to dgtal
More informationL-Edge Chromatic Number Of A Graph
IJISET - Internatona Journa of Innovatve Scence Engneerng & Technoogy Vo. 3 Issue 3 March 06. ISSN 348 7968 L-Edge Chromatc Number Of A Graph Dr.R.B.Gnana Joth Assocate Professor of Mathematcs V.V.Vannaperuma
More informationTHE METRIC DIMENSION OF AMALGAMATION OF CYCLES
Far East Journa of Mathematca Scences (FJMS) Voume 4 Number 00 Pages 9- Ths paper s avaabe onne at http://pphm.com/ournas/fms.htm 00 Pushpa Pubshng House THE METRIC DIMENSION OF AMALGAMATION OF CYCLES
More informationA Robust Method for Calculating the Correlation Coefficient
A Robust Method for Calculatng the Correlaton Coeffcent E.B. Nven and C. V. Deutsch Relatonshps between prmary and secondary data are frequently quantfed usng the correlaton coeffcent; however, the tradtonal
More informationEvaluation of simple performance measures for tuning SVM hyperparameters
Evaluaton of smple performance measures for tunng SVM hyperparameters Kabo Duan, S Sathya Keerth, Aun Neow Poo Department of Mechancal Engneerng, Natonal Unversty of Sngapore, 0 Kent Rdge Crescent, 960,
More informationSupport Vector Machines CS434
Support Vector Machnes CS434 Lnear Separators Many lnear separators exst that perfectly classfy all tranng examples Whch of the lnear separators s the best? + + + + + + + + + Intuton of Margn Consder ponts
More informationON THE BEHAVIOR OF THE CONJUGATE-GRADIENT METHOD ON ILL-CONDITIONED PROBLEMS
ON THE BEHAVIOR OF THE CONJUGATE-GRADIENT METHOD ON I-CONDITIONED PROBEM Anders FORGREN Technca Report TRITA-MAT-006-O Department of Mathematcs Roya Insttute of Technoogy January 006 Abstract We study
More information