Modeling of ship structural systems by events
|
|
- Erin Newton
- 5 years ago
- Views:
Transcription
1 UNIVERISTY OF SPLIT FACULTY OF ELECTRICAL ENGINEERING, MECHANICAL ENGINEERING AND NAVAL ARCHITECTURE Mdeling ship structural systems by events Brank Blagjević
2 Mtivatin Inclusin the cncept entrpy rm inrmatin thery as the nly ratinal measure system uncertainty, r the estimatin structural prperties. Rbustness and redundancy systems events may be cnsidered as additinal characteristics engineering systems (ship structures). The prblem distinctin cmplex engineering systems that have the same reliabilities and prbabilities ailure, but dierent number pssible events.
3 Event riented system analysis System events S E E... E 1... p E p E p E 1 n n Events E i, i = 1,,,n are STATES the system S. Entrpy Uncertainty individual randm event, E, with prbability ccurrence p(e) is measured by entrpy: H lg p E Entrpy a system events (Shannn): H( S ) H ( S ) H ( p, p,..., p ) p lg p n n 1 n i i i1 n
4 Types events particular interest r engineering purpses: Operatinal, E Failure, E Transitive, E t Cllapse, E c System events, S, can be subdivided int subsystems: peratinal and ailure O E E E 1 p E p E p E 1 N N F E E E N1 N NN p E p E p E N1 N NN
5 Then system, S, can be viewed cnditinally: S / O Entrpy a subsystem is: E / O E / O E / O E / O 1 N p E p E p E p E 1 N po po po p O E / F E / F E / F E / F N1 N N NN S / F p E p E p E p E N1 N N NN p( ) p( ) p( ) p( ) F F F F H m i mi p Eij S / Si lg p S j1 i i p E DOES NOT DEPEND n the prbability the system p(s) DOES NOT DEPEND whether the system is cmplete r incmplete p ij S
6 Rbustness Rbustness is regarded as the system s capability t respnd t all pssible randm ailures unirmly. The system rbustness is related nly t the ailure mdes the system: H N NN p Ei S / F lg p F in 1 p E p i F S / F S S / F ROB ROB H N ROB (S) = 0, i there is n ailure, r ne ailure event has a prbability p=1 ROB (S) = max when all the ailure mdes are equally prbable. Rbustness increases with increasing number events in the system
7 Redundancy capability a system t cntinue peratins by perrming dierent randm peratinal mdes given prbabilities in case randm ailures cmpnents The system redundancy is related nly t the peratinal mdes the system: H N N p Ei S / O lg p O i1 p E p i O S / O S S / O RED RED H N RED = 0 i there are n peratinal states r i nly ne peratinal state is pssible RED = max. i all peratinal states are equally prbable
8 Rbustness a beam Example 1 F y Mean COV Distributin Side a 6 mm 0,01 Nrmal Side b 5 mm 0,01 Nrmal b a x Length L 500 mm 0,01 Nrmal Mdulus elasticity E N/mm 0,01 Nrmal A = a b Yield stress F 5 N/mm 0,06 Lg- Nrmal L Lad (Frce) F t 150 kn 0, Nrmal Crss-sectin Area A 900 mm 0,1 Nrmal Critical buckling stress ( x ) Cx 0,4 N/mm 0,07 Lg-nrmal b a F Critical buckling stress ( y ) Cy 19, N/mm 0,07 Lg-nrmal Limit state unctins: Cmpressin: g 1 = A F F t Buckling (x): g = A Cx F t Buckling (y): g = A Cy F t A1 =,1511 A =, A =,15947
9 Example 1 Series system, basic events: A 1 A A Cmpund events E i = n =8 System events: E E E E E E E S 0,9897 8, ,510 8, , , , ,1,, 1, 1,, Reliability series system: R S pe 1 0, 9897 p S 0,01708 Uncnditinal entrpy: H(S) = 0,14191 (,80755; 0,047800) System rbustness: ROB S H S F i 7 p Ei p Ei N / lg 0, p F p F Maksimum rbustness: ROB max (S) = lg (N ) =,58496
10 Example 1 Event riented system analysis a beam Requirements: A = 900mm = cnst. L = 500 mm = cnst. Results: Max. ROB r a = b = 0 mm ROB max = 1,780
11 Fr a=b=0 mm cnsider the change L t rbustness.,5 Example 1 Cnditin: R (S) > 0,999 Result: ROB(S ), R(S ),0 1,5 1,0 0,5 R(S ) ROB(S ) ROB max r L = 4 mm 0, Beam length L, mm Cnclusins r example 1 Rbustness changes r dierent dimensins. It is pssible t calculate max. Rbustness Fr the same reliability level the rbustness varies signiicantly.
12 Example EOSA: Rbustness ship structural elements L = 17,15 m B = 1,4 m D = 11 m = tdw b e =80mm hw= 0mm t w tp Lads: DnV 4 ailure mdes Trsinal buckling Lcal buckling Plastic ailure Fatigue ailure
13 Series system (4 basic events) Example A 1 (trsinal buckling) A (lcal buckling) A (plastic dermatin) A 4 (atigue) System: E E 1 1,1 E, E, E4,4 E1, 0, ,95 10, , ,8 10,90 10 S E1, E1,4 E, E,4 E, , , ,0 10 1,85 10, Reliability: R (S) = 0,909 p (S) = 0,09014 Uncnditinal entrpy: H(S) = 0,44471 Rbustness: ROB (S) = 0,804 Max. Rbustness =,1
14 Analysis: Rbustness change r dierent lngitudinal s height and under cnditins: A = cnst. 10 mm < h w < 0 mm R > 0,909 Example 1,00 0,95 0,90 R(S ) ROB(S ), R(S ) 0,85 0,80 0,75 0,70 ROB(S ) 0,65 Cnclusins: 0, Lngitudinal's height h w, mm Rbustness a system events can be related t design variables ship structural elements max. ROB can be achieved within acceptable gemetry limits it is pssible t use ROB t cmpare dierent design slutins with varius cnstraints applied
15 Redundancy ship structures Example Deck panel (tanker) b b b tp 1 y' t w hw ht t t HP HP1 HP Functinal levels: b t tb 1. Level intact structure z'. Level ailure ne lngitudinal: n. r n.. Level ailure tw lngitudinals (nn-redundant structure) b b b tp 1 y' t w hw ht t t HP HP1 tb HP b t z'
16 Lads: DnV Failure mdes: buckling plating between stieners () plastic ailure a deck girder (1) plastic ailure lngitudinal () trsinal buckling a deck girder (1) trsinal buckling lngitudinal () Example 1st peratinal level: n = 11 basic events, nd peratinal level: S S S S S i 1 t 1 c N = 11 = 048 cmpund events S S, S E,..., S E,..., S E, S 1 i 1 t 1 t 1 t 1 c 1 1 j j 1 t 1 t N N 15 peratinal states, N = 971 cmpund events rd peratinal level 18 peratinal states, N = i 1 c 1 t 1 t 1 t S S 1S E1 S E 15S E15 t 1 t t 1 t t 1 t 1S E1 E1 S E E1 S E E1 t 1 t t 1 t t 1 t S 4S E4 E 5S E5 E 6S E6 E S E E S E E S E E t 1 t t 1 t t 1 t
17 Operatinal levels, states and transitive events a system 1 S = 1 1 S i 1 1S c 1 1S t 1 E t 1 1 E t 1 E t 1 E t 4 1 E t 5 1 E t 6 1 E t 7 1 E t 8 1 E t 9 1 E t 10 1 E t 11 1 E t 1 1 E t 1 1 E t 14 1 E t 15 1 S S S 4 S 5 S 6 S 7 S 8 S 9 S 10 S 11 S 1 S 1 S 14 S 15 S S = 1 1 S i 1 1S c 1 S S 5 S 6 S 7 S 1 E t S 1 E t 1 1 E t 4 S 1 E t 4 1 E t 5 1 E t 6 1 E t 7 1 E t 9 S 1 E t E t 10 1 E t 11 1 E t 1 1 E t 1 1 E t 14 8 S 10 S 11 S 1 S 1 S 14 S 15 S 1 E t 15 E t 1 E t E t E t 7 E t 8 E t 9 E t 1 E t 14 E t 15 E t 16 E t 17 E t 18 E t 4 E t 5 E t 6 E t 10 E t 11 E t 1 1 S S S 7 S 8 S 9 S 1 S 14 S 15 S 16 S 17 S 18 S 4 S 5 S 6 S 10 S 11 S 1 S S = 1 1 S i 1 1S i ( 1S E t 1) 1 E t 1 ( 4S E t 4) 1 E t ( 7S E t 7) 1 E t ( 10S E t 10) 1 E t 4 ( 1S E t 1) 1 E t 6 ( 16S E t 16) 1 E t 9 ( S E t ) 1 E t 1 ( 5S E t 5) 1 E t ( 8S E t 8) 1 E t ( 11S E t 11) 1 E t 4 ( 14S E t 14) 1 E t 6 ( 17S E t 17) 1 E t 9 ( S E t ) 1 E t 1 ( 6S E t 6) 1 E t ( 9S E t 9) 1 E t ( 1S E t 1) 1 E t 4 ( 15S E t 15) 1 E t 6 ( 18S E t 18) 1 E t 9
18 Analysis: Changes the redundancy r dierent spacing between lngitudinals. Cnstraints: Reliability must be equal r larger than that the riginal structural cniguratin. Weight the panel = cnst. Example 1,8 1,6 1,4 RED S i Result: R, RED 1, 1 0,8 R RED max = 1, ,6 0,4 0, Spacing between lngitudinals [mm]
19 Cnclusins Traditinal prbabilistic engineering system analysis based n physical and/r technical cmpnents a system, may be extended by an EOSA. Numerical examples cnirm the relevance EOSA and indicate ptential imprvements in system design (ROB, RED). Prblems Pssible numerical prblems when dealing with larger systems. Fr a cmplete event riented system analysis an enumeratin ALL the pssible events is needed.
20 General remarks 1. General relatins amng the prbability, uncertainty the system and uncertainties the subsystems are derived by using inrmatin thery.. The uncertainties in system s peratin riginate rm the unpredictability pssible events.. The system uncertainty analysis is based n entrpy. 4. The entrpy, as the nly ratinal measure system uncertainty, des nt depend n anything else ther than pssible events and in this sense is entirely bjective. 5. The entrpy a system itsel in general is nt particularly helpul in the assessment system perrmance. 6. The uncertainties imprtant subsystems events, such as the peratinal and ailure mdes, as well as their relatins t the uncertainty and reliability the entire system, can prvide a better insight int the system perrmance. 7. May be helpul in dierent ields engineering in the reinement system perrmance.
Computational modeling techniques
Cmputatinal mdeling techniques Lecture 4: Mdel checing fr ODE mdels In Petre Department f IT, Åb Aademi http://www.users.ab.fi/ipetre/cmpmd/ Cntent Stichimetric matrix Calculating the mass cnservatin relatins
More informationCourse Stabilty of Structures
Curse Stabilty f Structures Lecture ntes 2015.03.06 abut 3D beams, sme preliminaries (1:st rder thery) Trsin, 1:st rder thery 3D beams 2:nd rder thery Trsinal buckling Cupled buckling mdes, eamples Numerical
More informationFundamental Concepts in Structural Plasticity
Lecture Fundamental Cncepts in Structural Plasticit Prblem -: Stress ield cnditin Cnsider the plane stress ield cnditin in the principal crdinate sstem, a) Calculate the maximum difference between the
More information7 TH GRADE MATH STANDARDS
ALGEBRA STANDARDS Gal 1: Students will use the language f algebra t explre, describe, represent, and analyze number expressins and relatins 7 TH GRADE MATH STANDARDS 7.M.1.1: (Cmprehensin) Select, use,
More informationLecture 24: Flory-Huggins Theory
Lecture 24: 12.07.05 Flry-Huggins Thery Tday: LAST TIME...2 Lattice Mdels f Slutins...2 ENTROPY OF MIXING IN THE FLORY-HUGGINS MODEL...3 CONFIGURATIONS OF A SINGLE CHAIN...3 COUNTING CONFIGURATIONS FOR
More informationL a) Calculate the maximum allowable midspan deflection (w o ) critical under which the beam will slide off its support.
ecture 6 Mderately arge Deflectin Thery f Beams Prblem 6-1: Part A: The department f Highways and Public Wrks f the state f Califrnia is in the prcess f imprving the design f bridge verpasses t meet earthquake
More informationEquilibrium of Stress
Equilibrium f Stress Cnsider tw perpendicular planes passing thrugh a pint p. The stress cmpnents acting n these planes are as shwn in ig. 3.4.1a. These stresses are usuall shwn tgether acting n a small
More informationChapter 3: Cluster Analysis
Chapter 3: Cluster Analysis } 3.1 Basic Cncepts f Clustering 3.1.1 Cluster Analysis 3.1. Clustering Categries } 3. Partitining Methds 3..1 The principle 3.. K-Means Methd 3..3 K-Medids Methd 3..4 CLARA
More informationComputational modeling techniques
Cmputatinal mdeling techniques Lecture 2: Mdeling change. In Petre Department f IT, Åb Akademi http://users.ab.fi/ipetre/cmpmd/ Cntent f the lecture Basic paradigm f mdeling change Examples Linear dynamical
More informationINTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 1, No 3, 2010
Prbabilistic Analysis f Lateral Displacements f Shear in a 20 strey building Samir Benaissa 1, Belaid Mechab 2 1 Labratire de Mathematiques, Université de Sidi Bel Abbes BP 89, Sidi Bel Abbes 22000, Algerie.
More informationChecking the resolved resonance region in EXFOR database
Checking the reslved resnance regin in EXFOR database Gttfried Bertn Sciété de Calcul Mathématique (SCM) Oscar Cabells OECD/NEA Data Bank JEFF Meetings - Sessin JEFF Experiments Nvember 0-4, 017 Bulgne-Billancurt,
More informationComputational modeling techniques
Cmputatinal mdeling techniques Lecture 3: Mdeling change (2) Mdeling using prprtinality Mdeling using gemetric similarity In Petre Department f IT, Ab Akademi http://www.users.ab.fi/ipetre/cmpmd/ http://users.ab.fi/ipetre/cmpmd/
More informationFundamental concept of metal rolling
Fundamental cncept metal rlling Assumptins 1) Te arc cntact between te rlls and te metal is a part a circle. v x x α L p y y R v 2) Te ceicient rictin, µ, is cnstant in tery, but in reality µ varies alng
More informationBootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) >
Btstrap Methd > # Purpse: understand hw btstrap methd wrks > bs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(bs) > mean(bs) [1] 21.64625 > # estimate f lambda > lambda = 1/mean(bs);
More information22.54 Neutron Interactions and Applications (Spring 2004) Chapter 11 (3/11/04) Neutron Diffusion
.54 Neutrn Interactins and Applicatins (Spring 004) Chapter (3//04) Neutrn Diffusin References -- J. R. Lamarsh, Intrductin t Nuclear Reactr Thery (Addisn-Wesley, Reading, 966) T study neutrn diffusin
More informationCS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007
CS 477/677 Analysis f Algrithms Fall 2007 Dr. Gerge Bebis Curse Prject Due Date: 11/29/2007 Part1: Cmparisn f Srting Algrithms (70% f the prject grade) The bjective f the first part f the assignment is
More informationThermodynamics Partial Outline of Topics
Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)
More informationThe Kullback-Leibler Kernel as a Framework for Discriminant and Localized Representations for Visual Recognition
The Kullback-Leibler Kernel as a Framewrk fr Discriminant and Lcalized Representatins fr Visual Recgnitin Nun Vascncels Purdy H Pedr Mren ECE Department University f Califrnia, San Dieg HP Labs Cambridge
More informationA Study on Pullout Strength of Cast-in-place Anchor bolt in Concrete under High Temperature
Transactins f the 7 th Internatinal Cnference n Structural Mechanics in Reactr Technlgy (SMiRT 7) Prague, Czech Republic, August 7 22, 23 Paper #H-2 A Study n Pullut Strength f Cast-in-place Anchr blt
More informationTransduction Based on Changes in the Energy Stored in an Electrical Field
Lecture 6-3 Transductin Based n Changes in the Energy Stred in an Electrical ield Department f Mechanical Engineering Example:Capacitive Pressure Sensr Pressure sensitive capacitive device With separatin
More information3. Design of Channels General Definition of some terms CHAPTER THREE
CHAPTER THREE. Design f Channels.. General The success f the irrigatin system depends n the design f the netwrk f canals. The canals may be excavated thrugh the difference types f sils such as alluvial
More informationMidwest Big Data Summer School: Machine Learning I: Introduction. Kris De Brabanter
Midwest Big Data Summer Schl: Machine Learning I: Intrductin Kris De Brabanter kbrabant@iastate.edu Iwa State University Department f Statistics Department f Cmputer Science June 24, 2016 1/24 Outline
More informationLecture 6: Phase Space and Damped Oscillations
Lecture 6: Phase Space and Damped Oscillatins Oscillatins in Multiple Dimensins The preius discussin was fine fr scillatin in a single dimensin In general, thugh, we want t deal with the situatin where:
More informationEmphases in Common Core Standards for Mathematical Content Kindergarten High School
Emphases in Cmmn Cre Standards fr Mathematical Cntent Kindergarten High Schl Cntent Emphases by Cluster March 12, 2012 Describes cntent emphases in the standards at the cluster level fr each grade. These
More informationMODULE ONE. This module addresses the foundational concepts and skills that support all of the Elementary Algebra academic standards.
Mdule Fundatinal Tpics MODULE ONE This mdule addresses the fundatinal cncepts and skills that supprt all f the Elementary Algebra academic standards. SC Academic Elementary Algebra Indicatrs included in
More information^YawataR&D Laboratory, Nippon Steel Corporation, Tobata, Kitakyushu, Japan
Detectin f fatigue crack initiatin frm a ntch under a randm lad C. Makabe," S. Nishida^C. Urashima,' H. Kaneshir* "Department f Mechanical Systems Engineering, University f the Ryukyus, Nishihara, kinawa,
More informationAN INTERMITTENTLY USED SYSTEM WITH PREVENTIVE MAINTENANCE
J. Operatins Research Sc. f Japan V!. 15, N. 2, June 1972. 1972 The Operatins Research Sciety f Japan AN INTERMITTENTLY USED SYSTEM WITH PREVENTIVE MAINTENANCE SHUNJI OSAKI University f Suthern Califrnia
More information[COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t o m a k e s u r e y o u a r e r e a d y )
(Abut the final) [COLLEGE ALGEBRA EXAM I REVIEW TOPICS] ( u s e t h i s t m a k e s u r e y u a r e r e a d y ) The department writes the final exam s I dn't really knw what's n it and I can't very well
More informationBuilding to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems.
Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve real-wrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define
More informationSurface and Contact Stress
Surface and Cntact Stress The cncept f the frce is fundamental t mechanics and many imprtant prblems can be cast in terms f frces nly, fr example the prblems cnsidered in Chapter. Hwever, mre sphisticated
More informationNOTE ON THE ANALYSIS OF A RANDOMIZED BLOCK DESIGN. Junjiro Ogawa University of North Carolina
NOTE ON THE ANALYSIS OF A RANDOMIZED BLOCK DESIGN by Junjir Ogawa University f Nrth Carlina This research was supprted by the Office f Naval Research under Cntract N. Nnr-855(06) fr research in prbability
More information1 The limitations of Hartree Fock approximation
Chapter: Pst-Hartree Fck Methds - I The limitatins f Hartree Fck apprximatin The n electrn single determinant Hartree Fck wave functin is the variatinal best amng all pssible n electrn single determinants
More informationMATHEMATICS SYLLABUS SECONDARY 5th YEAR
Eurpean Schls Office f the Secretary-General Pedaggical Develpment Unit Ref. : 011-01-D-8-en- Orig. : EN MATHEMATICS SYLLABUS SECONDARY 5th YEAR 6 perid/week curse APPROVED BY THE JOINT TEACHING COMMITTEE
More informationModule 4: General Formulation of Electric Circuit Theory
Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated
More informationEric Klein and Ning Sa
Week 12. Statistical Appraches t Netwrks: p1 and p* Wasserman and Faust Chapter 15: Statistical Analysis f Single Relatinal Netwrks There are fur tasks in psitinal analysis: 1) Define Equivalence 2) Measure
More informationPart 3 Introduction to statistical classification techniques
Part 3 Intrductin t statistical classificatin techniques Machine Learning, Part 3, March 07 Fabi Rli Preamble ØIn Part we have seen that if we knw: Psterir prbabilities P(ω i / ) Or the equivalent terms
More informationENGI 4430 Parametric Vector Functions Page 2-01
ENGI 4430 Parametric Vectr Functins Page -01. Parametric Vectr Functins (cntinued) Any nn-zer vectr r can be decmpsed int its magnitude r and its directin: r rrˆ, where r r 0 Tangent Vectr: dx dy dz dr
More informationLecture 23: Lattice Models of Materials; Modeling Polymer Solutions
Lecture 23: 12.05.05 Lattice Mdels f Materials; Mdeling Plymer Slutins Tday: LAST TIME...2 The Bltzmann Factr and Partitin Functin: systems at cnstant temperature...2 A better mdel: The Debye slid...3
More informationCHAPTER 8b Static Equilibrium Units
CHAPTER 8b Static Equilibrium Units The Cnditins fr Equilibrium Slving Statics Prblems Stability and Balance Elasticity; Stress and Strain The Cnditins fr Equilibrium An bject with frces acting n it, but
More informationCONSTRUCTING STATECHART DIAGRAMS
CONSTRUCTING STATECHART DIAGRAMS The fllwing checklist shws the necessary steps fr cnstructing the statechart diagrams f a class. Subsequently, we will explain the individual steps further. Checklist 4.6
More informationEcology 302 Lecture III. Exponential Growth (Gotelli, Chapter 1; Ricklefs, Chapter 11, pp )
Eclgy 302 Lecture III. Expnential Grwth (Gtelli, Chapter 1; Ricklefs, Chapter 11, pp. 222-227) Apcalypse nw. The Santa Ana Watershed Prject Authrity pulls n punches in prtraying its missin in apcalyptic
More informationOn Boussinesq's problem
Internatinal Jurnal f Engineering Science 39 (2001) 317±322 www.elsevier.cm/lcate/ijengsci On Bussinesq's prblem A.P.S. Selvadurai * Department f Civil Engineering and Applied Mechanics, McGill University,
More informationFIELD QUALITY IN ACCELERATOR MAGNETS
FIELD QUALITY IN ACCELERATOR MAGNETS S. Russenschuck CERN, 1211 Geneva 23, Switzerland Abstract The field quality in the supercnducting magnets is expressed in terms f the cefficients f the Furier series
More information, which yields. where z1. and z2
The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin
More informationModelling of Clock Behaviour. Don Percival. Applied Physics Laboratory University of Washington Seattle, Washington, USA
Mdelling f Clck Behaviur Dn Percival Applied Physics Labratry University f Washingtn Seattle, Washingtn, USA verheads and paper fr talk available at http://faculty.washingtn.edu/dbp/talks.html 1 Overview
More informationCOMP 551 Applied Machine Learning Lecture 4: Linear classification
COMP 551 Applied Machine Learning Lecture 4: Linear classificatin Instructr: Jelle Pineau (jpineau@cs.mcgill.ca) Class web page: www.cs.mcgill.ca/~jpineau/cmp551 Unless therwise nted, all material psted
More informationCOMP 551 Applied Machine Learning Lecture 5: Generative models for linear classification
COMP 551 Applied Machine Learning Lecture 5: Generative mdels fr linear classificatin Instructr: Herke van Hf (herke.vanhf@mail.mcgill.ca) Slides mstly by: Jelle Pineau Class web page: www.cs.mcgill.ca/~hvanh2/cmp551
More informationChapter 17 Free Energy and Thermodynamics
Chemistry: A Mlecular Apprach, 1 st Ed. Nivald Tr Chapter 17 Free Energy and Thermdynamics Ry Kennedy Massachusetts Bay Cmmunity Cllege Wellesley Hills, MA 2008, Prentice Hall First Law f Thermdynamics
More informationResampling Methods. Cross-validation, Bootstrapping. Marek Petrik 2/21/2017
Resampling Methds Crss-validatin, Btstrapping Marek Petrik 2/21/2017 Sme f the figures in this presentatin are taken frm An Intrductin t Statistical Learning, with applicatins in R (Springer, 2013) with
More informationLecture 5: Equilibrium and Oscillations
Lecture 5: Equilibrium and Oscillatins Energy and Mtin Last time, we fund that fr a system with energy cnserved, v = ± E U m ( ) ( ) One result we see immediately is that there is n slutin fr velcity if
More information[ ] [ ] [ ] [ ] [ ] [ J] dt x x hard to solve in general solve it numerically. If there is no convection. is in the absence of reaction n
.3 The material balance equatin Net change f [J] due t diffusin, cnvectin, and reactin [ ] [ ] [ ] d J J J n = D v k [ J ] fr n - th reactin dt x x hard t slve in general slve it numerically If there is
More informationMath Foundations 20 Work Plan
Math Fundatins 20 Wrk Plan Units / Tpics 20.8 Demnstrate understanding f systems f linear inequalities in tw variables. Time Frame December 1-3 weeks 6-10 Majr Learning Indicatrs Identify situatins relevant
More informationNGSS High School Physics Domain Model
NGSS High Schl Physics Dmain Mdel Mtin and Stability: Frces and Interactins HS-PS2-1: Students will be able t analyze data t supprt the claim that Newtn s secnd law f mtin describes the mathematical relatinship
More informationk-nearest Neighbor How to choose k Average of k points more reliable when: Large k: noise in attributes +o o noise in class labels
Mtivating Example Memry-Based Learning Instance-Based Learning K-earest eighbr Inductive Assumptin Similar inputs map t similar utputs If nt true => learning is impssible If true => learning reduces t
More informationThermodynamics and Equilibrium
Thermdynamics and Equilibrium Thermdynamics Thermdynamics is the study f the relatinship between heat and ther frms f energy in a chemical r physical prcess. We intrduced the thermdynamic prperty f enthalpy,
More informationYou need to be able to define the following terms and answer basic questions about them:
CS440/ECE448 Sectin Q Fall 2017 Midterm Review Yu need t be able t define the fllwing terms and answer basic questins abut them: Intr t AI, agents and envirnments Pssible definitins f AI, prs and cns f
More informationCompetency Statements for Wm. E. Hay Mathematics for grades 7 through 12:
Cmpetency Statements fr Wm. E. Hay Mathematics fr grades 7 thrugh 12: Upn cmpletin f grade 12 a student will have develped a cmbinatin f sme/all f the fllwing cmpetencies depending upn the stream f math
More informationMECHANICS OF SOLIDS TORSION TUTORIAL 2 TORSION OF THIN WALLED SECTIONS AND THIN STRIPS
MECHANICS OF SOLIDS ORSION UORIAL ORSION OF HIN WALLED SECIONS AND HIN SRIPS Yu shuld judge yur prgress by cmpleting the self assessment exercises. On cmpletin f this tutrial yu shuld be able t d the fllwing.
More informationSodium D-line doublet. Lectures 5-6: Magnetic dipole moments. Orbital magnetic dipole moments. Orbital magnetic dipole moments
Lectures 5-6: Magnetic diple mments Sdium D-line dublet Orbital diple mments. Orbital precessin. Grtrian diagram fr dublet states f neutral sdium shwing permitted transitins, including Na D-line transitin
More informationMore Tutorial at
Answer each questin in the space prvided; use back f page if extra space is needed. Answer questins s the grader can READILY understand yur wrk; nly wrk n the exam sheet will be cnsidered. Write answers,
More informationDistributions, spatial statistics and a Bayesian perspective
Distributins, spatial statistics and a Bayesian perspective Dug Nychka Natinal Center fr Atmspheric Research Distributins and densities Cnditinal distributins and Bayes Thm Bivariate nrmal Spatial statistics
More informationHypothesis Tests for One Population Mean
Hypthesis Tests fr One Ppulatin Mean Chapter 9 Ala Abdelbaki Objective Objective: T estimate the value f ne ppulatin mean Inferential statistics using statistics in rder t estimate parameters We will be
More informationLesson Plan. Recode: They will do a graphic organizer to sequence the steps of scientific method.
Lessn Plan Reach: Ask the students if they ever ppped a bag f micrwave ppcrn and nticed hw many kernels were unppped at the bttm f the bag which made yu wnder if ther brands pp better than the ne yu are
More informationELE Final Exam - Dec. 2018
ELE 509 Final Exam Dec 2018 1 Cnsider tw Gaussian randm sequences X[n] and Y[n] Assume that they are independent f each ther with means and autcvariances μ ' 3 μ * 4 C ' [m] 1 2 1 3 and C * [m] 3 1 10
More informationResampling Methods. Chapter 5. Chapter 5 1 / 52
Resampling Methds Chapter 5 Chapter 5 1 / 52 1 51 Validatin set apprach 2 52 Crss validatin 3 53 Btstrap Chapter 5 2 / 52 Abut Resampling An imprtant statistical tl Pretending the data as ppulatin and
More information3. Mass Transfer with Chemical Reaction
8 3. Mass Transfer with Chemical Reactin 3. Mass Transfer with Chemical Reactin In the fllwing, the fundamentals f desrptin with chemical reactin, which are applied t the prblem f CO 2 desrptin in ME distillers,
More informationECEN 4872/5827 Lecture Notes
ECEN 4872/5827 Lecture Ntes Lecture #5 Objectives fr lecture #5: 1. Analysis f precisin current reference 2. Appraches fr evaluating tlerances 3. Temperature Cefficients evaluatin technique 4. Fundamentals
More informationProbability, Random Variables, and Processes. Probability
Prbability, Randm Variables, and Prcesses Prbability Prbability Prbability thery: branch f mathematics fr descriptin and mdelling f randm events Mdern prbability thery - the aximatic definitin f prbability
More informationTree Structured Classifier
Tree Structured Classifier Reference: Classificatin and Regressin Trees by L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stne, Chapman & Hall, 98. A Medical Eample (CART): Predict high risk patients
More information(1.1) V which contains charges. If a charge density ρ, is defined as the limit of the ratio of the charge contained. 0, and if a force density f
1.0 Review f Electrmagnetic Field Thery Selected aspects f electrmagnetic thery are reviewed in this sectin, with emphasis n cncepts which are useful in understanding magnet design. Detailed, rigrus treatments
More informationMultiobjective Evolutionary Optimization
Multibjective Evlutinary Optimizatin Pressr Qingu ZHANG Schl Cmputer Science and Electrnic Engineering University Essex CO4 3SQ, Clchester UK Outline Multibjective Optimisatin Paret Dminance Based Algrithms
More informationTypes of Energy COMMON MISCONCEPTIONS CHEMICAL REACTIONS INVOLVE ENERGY
CHEMICAL REACTIONS INVOLVE ENERGY The study energy and its transrmatins is knwn as thermdynamics. The discussin thermdynamics invlve the cncepts energy, wrk, and heat. Types Energy Ptential energy is stred
More informationSMART TESTING BOMBARDIER THOUGHTS
Bmbardier Inc. u ses filiales. Tus drits réservés. BOMBARDIER THOUGHTS FAA Bmbardier Wrkshp Mntreal 15-18 th September 2015 Bmbardier Inc. u ses filiales. Tus drits réservés. LEVERAGING ANALYSIS METHODS
More informationDetermining the Accuracy of Modal Parameter Estimation Methods
Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system
More informationMODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards:
MODULE FOUR This mdule addresses functins SC Academic Standards: EA-3.1 Classify a relatinship as being either a functin r nt a functin when given data as a table, set f rdered pairs, r graph. EA-3.2 Use
More informationPOLARISATION VISUAL PHYSICS ONLINE. View video on polarisation of light
VISUAL PHYSICS ONLINE MODULE 7 NATURE OF LIGHT POLARISATION View vide n plarisatin f light While all the experimental evidence s far that supprts the wave nature f light, nne f it tells us whether light
More informationChapter Summary. Mathematical Induction Strong Induction Recursive Definitions Structural Induction Recursive Algorithms
Chapter 5 1 Chapter Summary Mathematical Inductin Strng Inductin Recursive Definitins Structural Inductin Recursive Algrithms Sectin 5.1 3 Sectin Summary Mathematical Inductin Examples f Prf by Mathematical
More informationChapter 2 GAUSS LAW Recommended Problems:
Chapter GAUSS LAW Recmmended Prblems: 1,4,5,6,7,9,11,13,15,18,19,1,7,9,31,35,37,39,41,43,45,47,49,51,55,57,61,6,69. LCTRIC FLUX lectric flux is a measure f the number f electric filed lines penetrating
More informationLecture 10, Principal Component Analysis
Principal Cmpnent Analysis Lecture 10, Principal Cmpnent Analysis Ha Helen Zhang Fall 2017 Ha Helen Zhang Lecture 10, Principal Cmpnent Analysis 1 / 16 Principal Cmpnent Analysis Lecture 10, Principal
More informationPublic Key Cryptography. Tim van der Horst & Kent Seamons
Public Key Cryptgraphy Tim van der Hrst & Kent Seamns Last Updated: Oct 5, 2017 Asymmetric Encryptin Why Public Key Crypt is Cl Has a linear slutin t the key distributin prblem Symmetric crypt has an expnential
More informationOn Huntsberger Type Shrinkage Estimator for the Mean of Normal Distribution ABSTRACT INTRODUCTION
Malaysian Jurnal f Mathematical Sciences 4(): 7-4 () On Huntsberger Type Shrinkage Estimatr fr the Mean f Nrmal Distributin Department f Mathematical and Physical Sciences, University f Nizwa, Sultanate
More informationAerodynamic Separability in Tip Speed Ratio and Separability in Wind Speed- a Comparison
Jurnal f Physics: Cnference Series OPEN ACCESS Aerdynamic Separability in Tip Speed Rati and Separability in Wind Speed- a Cmparisn T cite this article: M L Gala Sants et al 14 J. Phys.: Cnf. Ser. 555
More informationand for compressible flow
57: Mechanics Flids and Transprt Prcesses Chapter 9 Pressr Fred Stern Typed by Stephanie Schrader Fall 999 9.5 Qantitative Relatins r the Trblent Bndary ayer Descriptin Trblent Flw V and p are randm nctins
More informationA New Evaluation Measure. J. Joiner and L. Werner. The problems of evaluation and the needed criteria of evaluation
III-l III. A New Evaluatin Measure J. Jiner and L. Werner Abstract The prblems f evaluatin and the needed criteria f evaluatin measures in the SMART system f infrmatin retrieval are reviewed and discussed.
More informationOn Topological Structures and. Fuzzy Sets
L - ZHR UNIVERSIT - GZ DENSHIP OF GRDUTE STUDIES & SCIENTIFIC RESERCH On Tplgical Structures and Fuzzy Sets y Nashaat hmed Saleem Raab Supervised by Dr. Mhammed Jamal Iqelan Thesis Submitted in Partial
More informationLim f (x) e. Find the largest possible domain and its discontinuity points. Why is it discontinuous at those points (if any)?
THESE ARE SAMPLE QUESTIONS FOR EACH OF THE STUDENT LEARNING OUTCOMES (SLO) SET FOR THIS COURSE. SLO 1: Understand and use the cncept f the limit f a functin i. Use prperties f limits and ther techniques,
More informationQ1. A string of length L is fixed at both ends. Which one of the following is NOT a possible wavelength for standing waves on this string?
Term: 111 Thursday, January 05, 2012 Page: 1 Q1. A string f length L is fixed at bth ends. Which ne f the fllwing is NOT a pssible wavelength fr standing waves n this string? Q2. λ n = 2L n = A) 4L B)
More informationRevisiting the Socrates Example
Sectin 1.6 Sectin Summary Valid Arguments Inference Rules fr Prpsitinal Lgic Using Rules f Inference t Build Arguments Rules f Inference fr Quantified Statements Building Arguments fr Quantified Statements
More informationOF SIMPLY SUPPORTED PLYWOOD PLATES UNDER COMBINED EDGEWISE BENDING AND COMPRESSION
U. S. FOREST SERVICE RESEARCH PAPER FPL 50 DECEMBER U. S. DEPARTMENT OF AGRICULTURE FOREST SERVICE FOREST PRODUCTS LABORATORY OF SIMPLY SUPPORTED PLYWOOD PLATES UNDER COMBINED EDGEWISE BENDING AND COMPRESSION
More informationSource Coding and Compression
Surce Cding and Cmpressin Heik Schwarz Cntact: Dr.-Ing. Heik Schwarz heik.schwarz@hhi.fraunhfer.de Heik Schwarz Surce Cding and Cmpressin September 22, 2013 1 / 60 PartI: Surce Cding Fundamentals Heik
More informationFormal Uncertainty Assessment in Aquarius Salinity Retrieval Algorithm
Frmal Uncertainty Assessment in Aquarius Salinity Retrieval Algrithm T. Meissner Aquarius Cal/Val Meeting Santa Rsa March 31/April 1, 2015 Outline 1. Backgrund/Philsphy 2. Develping an Algrithm fr Assessing
More informationPattern Recognition 2014 Support Vector Machines
Pattern Recgnitin 2014 Supprt Vectr Machines Ad Feelders Universiteit Utrecht Ad Feelders ( Universiteit Utrecht ) Pattern Recgnitin 1 / 55 Overview 1 Separable Case 2 Kernel Functins 3 Allwing Errrs (Sft
More informationOptimization Programming Problems For Control And Management Of Bacterial Disease With Two Stage Growth/Spread Among Plants
Internatinal Jurnal f Engineering Science Inventin ISSN (Online): 9 67, ISSN (Print): 9 676 www.ijesi.rg Vlume 5 Issue 8 ugust 06 PP.0-07 Optimizatin Prgramming Prblems Fr Cntrl nd Management Of Bacterial
More informationThermal analysis of Aluminum alloy Piston
Internatinal Jurnal f Emerging Trends in Engineering Research (IJETER), Vl. 3 N.6, Pages : 511-515 (2015) Special Issue f NCTET 2K15 - Held n June 13, 2015 in SV Cllege f Engineering, Tirupati http://warse.rg/ijeter/static/pdf/issue/nctet2015sp90.pdf
More information205MPa and a modulus of elasticity E 207 GPa. The critical load 75kN. Gravity is vertically downward and the weight of link 3 is W3
ME 5 - Machine Design I Fall Semester 06 Name f Student: Lab Sectin Number: Final Exam. Open bk clsed ntes. Friday, December 6th, 06 ur name lab sectin number must be included in the spaces prvided at
More informationAristotle I PHIL301 Prof. Oakes Winthrop University updated: 3/14/14 8:48 AM
Aristtle I PHIL301 Prf. Oakes Winthrp University updated: 3/14/14 8:48 AM The Categries - The Categries is ne f several imprtant wrks by Aristtle n metaphysics. His tpic here is the classificatin f beings
More informationChapters 29 and 35 Thermochemistry and Chemical Thermodynamics
Chapters 9 and 35 Thermchemistry and Chemical Thermdynamics 1 Cpyright (c) 011 by Michael A. Janusa, PhD. All rights reserved. Thermchemistry Thermchemistry is the study f the energy effects that accmpany
More informationPhysical Layer: Outline
18-: Intrductin t Telecmmunicatin Netwrks Lectures : Physical Layer Peter Steenkiste Spring 01 www.cs.cmu.edu/~prs/nets-ece Physical Layer: Outline Digital Representatin f Infrmatin Characterizatin f Cmmunicatin
More information7.0 Heat Transfer in an External Laminar Boundary Layer
7.0 Heat ransfer in an Eternal Laminar Bundary Layer 7. Intrductin In this chapter, we will assume: ) hat the fluid prperties are cnstant and unaffected by temperature variatins. ) he thermal & mmentum
More informationENSC Discrete Time Systems. Project Outline. Semester
ENSC 49 - iscrete Time Systems Prject Outline Semester 006-1. Objectives The gal f the prject is t design a channel fading simulatr. Upn successful cmpletin f the prject, yu will reinfrce yur understanding
More information