The study of fault-diagnosis method of reciprocating compressor based on fuzzy fault tree theory Jian-Chun Gong 1, a, PENG-Fei Tian 2,b
|
|
- Martin Gibbs
- 6 years ago
- Views:
Transcription
1 Applied Mechaics ad Materials Olie: ISSN: Vols pp doi:04028/wwwscietificet/amm Tras Tech Publicatios Switzerlad The study of fault-diagosis method of reciprocatig compressor based o fuzzy fault tree theory Jia-Chu Gog a PENG-Fei Tia 2b 2 PaZhiHua Uiversity chia a cgog0@63com b tiapegfeisust@qqcom Keywords: reciprocatig compressor fuzzy set theory fault tree diagosis Abstract Sice workig coditio of reciprocatig compressor is awfully bad ad it has bigger risk i operatio ad higher fault rate it is of importace to study reciprocatig compressor fault Fault tree has bee established i this paper by aalyzig factors leadig reciprocatig compressor fault based o the method of fault tree 2 miimum cut sets leadig to reciprocatig compressor fault ca be gotte through qualitative aalyses o this fault tree the happeig probability of the top evet ca be calculated ad the importace of the basic evet s ca be aalyzed through quatitative aalysis The expert iquiry method combied with fuzzy sets theory is adopted to assess the happeig probability of the basic evets ad top evets Reciprocatig compressor is extesively used i may petroleum ad chemical eterprises for high compressio ratio of sigle stage ad high work efficiecy Oce the machies are abormal ad fault it will affect the ormal productio brig huge ecoomic loss Developmet of reciprocatig compressor fault diagosis fault elimiatio ca be ivisible the ormal operatio of the machie ca be esured ecoomic beefit be improved Applicatio of fuzzy fault tree theory ca effectively diagose reciprocatig compressor failure probability ad quickly idetify the predisposig factors causig failure Costructio of fault tree Fault Tree Aalysis called FTA method for short is a kid of aalysis method that refies system fault formatio reaso from geeral to part accordig to the dedrimers So it is aalysis tool for the complicated dyamic system desig factory test or field foud that the failure forms of reliability FTA method is desiged to ascertai the basic fault determiig the cause of the malfuctio the [2] probability of occurrece ad impact Costructio of fault tree i fault tree aalysis is the most basic the most crucial lik also the premise coditio of fault tree aalysis For the same system a differet fault trees will be built by differet people accordig to differet eeds ad differet trai of thought But i the process of establishmet of fault tree the fault effect failure mode ad failure mechaism aalysis must be aalysised Oce the top evet is idetified the fault tree will be layer-by-layer built For reciprocatig compressor the faults of the air valve pressure packig rig fault Pisto rig fault pisto ad pisto rod cylider fault cylider fault oil wiper fault are the mai failure evets Because each elemet i the system are relatively idepedet each compoet is treated as fault subsystem idetified as itermediate evet The fault tree ca be layer-by-layer built The evet code is as follows reciprocatig compressor failure as the top evet is expressed i T Valve fault i Epressure packig rig fault i E2; fault of pisto rig i e3; pisto ad pisto rod cylider fault i E4; Cylider fault i E5; oil wiper fault i E6; valve failure i E7; sprig failure i E8 valve plate surface debris 2 the valve fracture sprig 3 ier surface crack 4 improper selectio of sprig 5 sprig 6 pisto rod ad a packig rig frictio ad wear 7 filler rod ad the pisto rod seal failure 8 packig box temperature icreased 9 pisto rig gap too small 0 pisto rig [] [ 35] All rights reserved No part of cotets of this paper may be reproduced or trasmitted i ay form or by ay meas without the writte permissio of Tras Tech Publicatios wwwttpet (ID: Pesylvaia State Uiversity Uiversity Park USA-05/03/69:44:27
2 2650 Advaced Materials ad Process Techology tesio too large pisto ad pisto rod of the mechaical properties ad smoothess does ot meet the requiremets 2 the pisto rod ad the pisto are ot firmly coected 3 pisto rod positioig termial ad the cetral lie of the pisto verticality does ot meet the requiremets 4 coolig water system i short supply 5 lubricatio system oil supply shortage 6 suctio valve cavity leakage 7 Exhaust valve ammed or broke 8 oil wiper wear 9 scrapig the oil rig icorrectly istalled 20 pisto rod wor or scratched 2 rig side clearace abormalities Fig The effect fault tree diagram of reciprocatig compressor I the above fault tree model there is oly a sigle logical" or" door It is said that the output evet will occur whe oe or more of the iput evet occurs Therefore oce there is oe evet of the iput logic" or" door several itermediate evets its upper level failure evet will happe reciprocatig compressor will be ieffective [ 6] Fault tree aalysis of reciprocatig compressor ( Structure fuctio of fault tree Fault tree structure fuctio is to use simple mathematical expressios i the form of fault tree i order to simplify the fault tree operate by usig mathematical method diagosis ad deal with the fault by computer Figure shows the reciprocatig compressor fault tree by the OR door evet expressio its ( Y xi max( x x2 x2 structure fuctio expressed as i 2 2 Y x 2 i I xi Y i the formula express i i( (2 I the formula: x ( i 22 as the top evet status i as the bottom evet status decided x by i 2 completely(total of 2 states O the represetatio whe the system has a bottom evet occurs the top evet occurs As ca be see the reciprocatig compressor fault tree without too much logic algebra rules for simplificatio it ca be behid the fuzzy fault tree aalysis The qualitative aalysis ad the quatitative aalysis Qualitative aalysis of fault tree is calculated all miimal cut sets the mai methods of miimum cut set are determiat method structural method ad Boolea algebraic simplificatio methodi this paper the fault tree is trasformed ito a equivalet Boolea algebra equatio usig Boolea algebraic simplificatio method Reciprocatig Compressors is o the blik (T the formula is as T follows(3: 2 i i ( (3
3 Applied Mechaics ad Materials Vols K K2 K supposed as all the miimal cut sets of fault tree of kow fault tree =2If the Q ( kow basic probability is i P i i 22 the fault tree ( T top evet occurrece probability calculatio formula is as follows: T P K K Q i i K i 2 _ Ki K _ KiK Kk ( KK2 K i k ik (4 Because the probability of bottom evet is very small the type (4 depeds oly o the first The structure importat degree aalysis is the importace degree of aalysis of the basic evets Cosiderig the basic evet probability chages will give top evet occurrece probability ifluece this is the basic evet probability importace degree Usig the top evet occurrece probability fuctio is a liear fuctio of this ature idepedet evet probability importace degree coefficiet Qi of a partial derivative gives the basic Calculatio of fault tree evet occurrece probability The expert ivestigatio method is oe of the most commoly used methods to determie the probability of evet occurrece As the obect to obtai iformatio experts make udgmets assessmet ad predictio method relyig o their kowledge ad experiece Whe the expert use atural laguage such as wee small lesser medium biggish large prodigious to describe the basic probability as a result of these atural laguage with a certai ambiguity Basic probability ca ot use traditioal methods Therefore fuzzy set theory is employed to deal with these ucertai iformatio with the triagular fuzzy umber or trapezoid fuzzy umber replace the atural laguage the fuzzy umber expressio form as show i Figure 2 [ 7] Figure 2 Represets the atural laguage i the mathematical model For reciprocatig compressor system if the bottom evet probability of the" valve ed is determied by Fuzzy set ad Del Delphi method there are 4 maor steps: amely the selectio of experts make subective udgmets; expert atural laguage ito fuzzy umber; fuzzy umbers are trasformed ito fuzzy likelihood value; fuzzy probability value ito the fuzzy failure rate ca be estimated accordig to the followig steps ( expert to make subective udgmets choose 5 differet areas experts from valve desig costructio istallatio repair ad maagemet to form assessmet group ad udge the bottom evet probability o of valve ed or (2 Trasform the atural laguage ito fuzzy relatio Figure 2 is a atural laguage fuzzy umber forms its membership fuctio:
4 2652 Advaced Materials ad Process Techology f FL x 02 (02 x 03 (03 x x (04 x 05 0 ( others (5 f L x ( x x (02< x 03 0 ( others x 04 x 05 (05 x 06 (04 x x (06 x 07 f M f (05 x 06 F H 08 x 0 (07 x 08 ( others (7 0 ( others (8 Formula: subscript FL L M FH are respectively o behalf of small small medium ad largethe [ 89] opiio of differet experts is combied with fuzzy sets ad the average algorithm The cut sets of type (5 to (8 respectively hypothesis: FL [ f f 2 ] L [ l ] l2 M [ m ] m2 FH [ h ] h2 f f 2 l l2 m m2 h h2 are the set upper ad lower limit of type (5 to (8 For f FL (x whe ( x 02 / f 02 f ; similarly available: l l2 03 m 04 m h 05 h2 08 Expert group assessmet is small small medium large medium I the cut set expert group opiios of geeral fuzzy umber z: fhl M FLM HL max ffh fm ffl fm fl( x = 2 ( 04 ( 05 ( 02 ( 2(06 + ( 08 ( 05 (03 (9 Type (9 average fuzzy umber W: W (05 6(28 05 ( 032(056 (0 5 By fuzzy set extesio theory W is fuzzy sets To make W z z2 ( 032(056 so z z2 or The average fuzzy umber W relatio fuctio is: x 032 (032 x 042 (042 x 046 f F H ( 056 x (046 x ( others (3 Trasformer the fuzzy umbers ito fuzzy likelihood value The fuzzy probability value ( represets the expert o a give evet likelihood cofidece Based o the Cheg ad Hwag [7] proposed about fuzzy rakig method this paper trasforms the fuzzy umber ito The maximum fuzzy set ad the miimum fuzzy set is defied as: (6
5 Applied Mechaics ad Materials Vols x (0 x f max 0 ( others x (0 x (2 f max (3 0 ( others The possible values of Fuzzy umber fuzzy average: R ( W sup fw f max 0509(4 L ( W sup fw f mi (5 x So W fuzzy likelihood value for: R ( W L ( W T ( W (6 2 (4 Trasform ambiguity may value ito the fuzzy real efficiecy ( FFR I order to esure the real efficiecy ad fuzzy efficiecy cosistecy betwee the fuzzy values must be trasformed ito fuzzy real efficiecy ( 0 k FRE 0 k ( / (7 ( fuzzy failure rate of Fuzzy umber W( FFR the probability of valve plate surface 3 debris is equal to Ad so o other bottom evet probability of reciprocatig compressor fault tree ca be calculatedcalculate top evet occurrece probability ad the bottom evet probability importace degree fid out the most importat ifluece factors of reciprocatig compressor failure provide guidace for reciprocatig compressor repair ad maagemetimprove its safety ad reliabilitythis shows that the mai factors of Reciprocatig compressor failure is the valve ad pressure packig rig fault;the secod is the pisto rig pisto ad pisto rod ad the cylider faultthe results ca be used for the maiteace ad improvemet of reciprocatig compressor desig theory Coclusio Based o the fuzzy fault tree the author uses the combiatio of fuzzy set theory ad expert udgmet method aalysis the Reciprocatig Compressors Fault Tree of evets ad the probability of top evet qualitatively ad quatitatively effectively overcome the traditioal fault tree aalysis errors from the failure probability of basic evet as a precise value improve the Reciprocatig Compressors Fault Diagosis techique Refereces [] Jilog Zhag The research ad Applicatio of Fuzzy diagosis method for reciprocatig compressor[d]dalia Uiversity of Techology2005 I Chiese [2] DighuaShi Sogrui Wag The fault tree aalysis method ad theory [M] Beiig Normal Uiversity press993 [3] Jidog Dig Yulig Ji Reciprocatig gas compressor commo faults ad troubleshootig [J ] Chia Equipmet Egieerig2004: I Chiese [4] JiagZhu Quag zhi Lou A large reciprocatig compressor are examples of commo faults ad aalysis [J ] Compressor techology20046: I Chiese [5]Juchao Wu The reciprocatig compressor fault aalysis [J] Chemical equipmet techology : [6] Shi Wag equivalet Fuzzy mathematics applicatio i artificial itelligece [M] Mechaical Idustry Press99 [7] Che Shu-Je H Wag Chi G-Lai Fuzzy multi2ple attribute decisio makig method sad applicatios[m] Berli :Spriger-Verlag 990 : [8 ] L IN CHIN-TORNG WANG MAO-J IUN J Hybrid fault tree aalysis usig fuzzy set s [J ] Reliability Egi2eerig ad System Safety 997 (58 : x
6 Advaced Materials ad Process Techology 04028/wwwscietificet/AMM27-29 The Study of Fault-Diagosis Method of Reciprocatig Compressor Based o Fuzzy Fault Tree Theory 04028/wwwscietificet/AMM
Polynomial Functions and Their Graphs
Polyomial Fuctios ad Their Graphs I this sectio we begi the study of fuctios defied by polyomial expressios. Polyomial ad ratioal fuctios are the most commo fuctios used to model data, ad are used extesively
More informationResearch on Dependable level in Network Computing System Yongxia Li 1, a, Guangxia Xu 2,b and Shuangyan Liu 3,c
Applied Mechaics ad Materials Olie: 04-0-06 ISSN: 66-748, Vols. 53-57, pp 05-08 doi:0.408/www.scietific.et/amm.53-57.05 04 Tras Tech Publicatios, Switzerlad Research o Depedable level i Network Computig
More informationReliability model of organization management chain of South-to-North Water Diversion Project during construction period
Water Sciece ad Egieerig, Dec. 2008, Vol. 1, No. 4, 107-113 ISSN 1674-2370, http://kkb.hhu.edu.c, e-mail: wse@hhu.edu.c Reliability model of orgaizatio maagemet chai of South-to-North Water Diversio Project
More information62. Power series Definition 16. (Power series) Given a sequence {c n }, the series. c n x n = c 0 + c 1 x + c 2 x 2 + c 3 x 3 +
62. Power series Defiitio 16. (Power series) Give a sequece {c }, the series c x = c 0 + c 1 x + c 2 x 2 + c 3 x 3 + is called a power series i the variable x. The umbers c are called the coefficiets of
More informationDefinitions and Theorems. where x are the decision variables. c, b, and a are constant coefficients.
Defiitios ad Theorems Remember the scalar form of the liear programmig problem, Miimize, Subject to, f(x) = c i x i a 1i x i = b 1 a mi x i = b m x i 0 i = 1,2,, where x are the decisio variables. c, b,
More informationSELECTION OF DRILL FOR DRILLING WITH HIGH PRESSURE COOLANT USING ENTROPY AND COPRAS MCDM METHOD
U.P.B. Sci. Bull., Series D, Vol. 79, Iss. 4, 2017 ISSN 1454-2358 SELECTION OF DRILL FOR DRILLING WITH HIGH PRESSURE COOLANT USING ENTROPY AND COPRAS MCDM METHOD Jelea STANOJKOVIĆ 1, Miroslav RADOVANOVIĆ
More informationGrey Correlation Analysis of China's Electricity Imports and Its Influence Factors Hongjing Zhang 1, a, Feng Wang 1, b and Zhenkun Tian 1, c
Applied Mechaics ad Materials Olie: 203-0-3 ISSN: 662-7482, Vols. 448-453, pp 258-262 doi:0.4028/www.scietific.et/amm.448-453.258 204 Tras Tech Publicatios, Switzerlad Grey Correlatio Aalysis of Chia's
More informationComparison Study of Series Approximation. and Convergence between Chebyshev. and Legendre Series
Applied Mathematical Scieces, Vol. 7, 03, o. 6, 3-337 HIKARI Ltd, www.m-hikari.com http://d.doi.org/0.988/ams.03.3430 Compariso Study of Series Approimatio ad Covergece betwee Chebyshev ad Legedre Series
More informationA statistical method to determine sample size to estimate characteristic value of soil parameters
A statistical method to determie sample size to estimate characteristic value of soil parameters Y. Hojo, B. Setiawa 2 ad M. Suzuki 3 Abstract Sample size is a importat factor to be cosidered i determiig
More informationThe Choquet Integral with Respect to Fuzzy-Valued Set Functions
The Choquet Itegral with Respect to Fuzzy-Valued Set Fuctios Weiwei Zhag Abstract The Choquet itegral with respect to real-valued oadditive set fuctios, such as siged efficiecy measures, has bee used i
More informationTopic 9: Sampling Distributions of Estimators
Topic 9: Samplig Distributios of Estimators Course 003, 2016 Page 0 Samplig distributios of estimators Sice our estimators are statistics (particular fuctios of radom variables), their distributio ca be
More informationResearch on real time compensation of thermal errors of CNC lathe based on linear regression theory Qiu Yongliang
d Iteratioal Coferece o Machiery, Materials Egieerig, Chemical Egieerig ad Biotechology (MMECEB 015) Research o real time compesatio of thermal errors of CNC lathe based o liear regressio theory Qiu Yogliag
More informationResearch Article A Unified Weight Formula for Calculating the Sample Variance from Weighted Successive Differences
Discrete Dyamics i Nature ad Society Article ID 210761 4 pages http://dxdoiorg/101155/2014/210761 Research Article A Uified Weight Formula for Calculatig the Sample Variace from Weighted Successive Differeces
More informationDesign of distribution transformer loss meter considering the harmonic loss based on one side measurement method
3rd Iteratioal Coferece o Machiery, Materials ad Iformatio Techology Applicatios (ICMMITA 05) Desig of distributio trasformer loss meter cosiderig the harmoic loss based o oe side measuremet method HU
More informationAnalysis of the No-Load Characteristic of the Moving Coil Linear Compressor
Purdue Uiversity Purdue e-pubs Iteratioal Compressor Egieerig Coferece School of Mechaical Egieerig 008 Aalysis of the No-Load Characteristic of the Movig Coil Liear Compressor Yigbai Xie North Chia Electric
More informationCALCULATING FIBONACCI VECTORS
THE GENERALIZED BINET FORMULA FOR CALCULATING FIBONACCI VECTORS Stuart D Aderso Departmet of Physics, Ithaca College 953 Daby Road, Ithaca NY 14850, USA email: saderso@ithacaedu ad Dai Novak Departmet
More informationAlgorithm of Superposition of Boolean Functions Given with Truth Vectors
IJCSI Iteratioal Joural of Computer Sciece Issues, Vol 9, Issue 4, No, July ISSN (Olie: 694-84 wwwijcsiorg 9 Algorithm of Superpositio of Boolea Fuctios Give with Truth Vectors Aatoly Plotikov, Aleader
More informationThe target reliability and design working life
Safety ad Security Egieerig IV 161 The target reliability ad desig workig life M. Holický Kloker Istitute, CTU i Prague, Czech Republic Abstract Desig workig life ad target reliability levels recommeded
More informationInterval Intuitionistic Trapezoidal Fuzzy Prioritized Aggregating Operators and their Application to Multiple Attribute Decision Making
Iterval Ituitioistic Trapezoidal Fuzzy Prioritized Aggregatig Operators ad their Applicatio to Multiple Attribute Decisio Makig Xia-Pig Jiag Chogqig Uiversity of Arts ad Scieces Chia cqmaagemet@163.com
More informationProperties and Hypothesis Testing
Chapter 3 Properties ad Hypothesis Testig 3.1 Types of data The regressio techiques developed i previous chapters ca be applied to three differet kids of data. 1. Cross-sectioal data. 2. Time series data.
More information[ ] sin ( ) ( ) = 2 2 ( ) ( ) ( ) ˆ Mechanical Spectroscopy II
Solid State Pheomea Vol. 89 (003) pp 343-348 (003) Tras Tech Publicatios, Switzerlad doi:0.408/www.scietific.et/ssp.89.343 A New Impulse Mechaical Spectrometer to Study the Dyamic Mechaical Properties
More informationChimica Inorganica 3
himica Iorgaica Irreducible Represetatios ad haracter Tables Rather tha usig geometrical operatios, it is ofte much more coveiet to employ a ew set of group elemets which are matrices ad to make the rule
More informationAnalysis of Fuzzy Fault Tree using Intuitionstic Fuzzy Numbers
Neeraj Lata / Iteratioal Joural of Computer Sciece & Egieerig Techology (IJCSET) Aalysis of Fuzzy Fault Tree usig Ituitiostic Fuzzy Numbers Neeraj Lata Departmet of applied Scieces,TeerthakerMahaveer Uiversity,
More informationLive Line Measuring the Parameters of 220 kv Transmission Lines with Mutual Inductance in Hainan Power Grid
Egieerig, 213, 5, 146-151 doi:1.4236/eg.213.51b27 Published Olie Jauary 213 (http://www.scirp.org/joural/eg) Live Lie Measurig the Parameters of 22 kv Trasmissio Lies with Mutual Iductace i Haia Power
More informationOn an Application of Bayesian Estimation
O a Applicatio of ayesia Estimatio KIYOHARU TANAKA School of Sciece ad Egieerig, Kiki Uiversity, Kowakae, Higashi-Osaka, JAPAN Email: ktaaka@ifokidaiacjp EVGENIY GRECHNIKOV Departmet of Mathematics, auma
More informationTopic 9: Sampling Distributions of Estimators
Topic 9: Samplig Distributios of Estimators Course 003, 2018 Page 0 Samplig distributios of estimators Sice our estimators are statistics (particular fuctios of radom variables), their distributio ca be
More informationThe Growth of Functions. Theoretical Supplement
The Growth of Fuctios Theoretical Supplemet The Triagle Iequality The triagle iequality is a algebraic tool that is ofte useful i maipulatig absolute values of fuctios. The triagle iequality says that
More informationTopic 9: Sampling Distributions of Estimators
Topic 9: Samplig Distributios of Estimators Course 003, 2018 Page 0 Samplig distributios of estimators Sice our estimators are statistics (particular fuctios of radom variables), their distributio ca be
More informationIP Reference guide for integer programming formulations.
IP Referece guide for iteger programmig formulatios. by James B. Orli for 15.053 ad 15.058 This documet is iteded as a compact (or relatively compact) guide to the formulatio of iteger programs. For more
More informationReliability and Queueing
Copyright 999 Uiversity of Califoria Reliability ad Queueig by David G. Messerschmitt Supplemetary sectio for Uderstadig Networked Applicatios: A First Course, Morga Kaufma, 999. Copyright otice: Permissio
More informationWHAT IS THE PROBABILITY FUNCTION FOR LARGE TSUNAMI WAVES? ABSTRACT
WHAT IS THE PROBABILITY FUNCTION FOR LARGE TSUNAMI WAVES? Harold G. Loomis Hoolulu, HI ABSTRACT Most coastal locatios have few if ay records of tsuami wave heights obtaied over various time periods. Still
More informationSequences, Mathematical Induction, and Recursion. CSE 2353 Discrete Computational Structures Spring 2018
CSE 353 Discrete Computatioal Structures Sprig 08 Sequeces, Mathematical Iductio, ad Recursio (Chapter 5, Epp) Note: some course slides adopted from publisher-provided material Overview May mathematical
More informationLecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting
Lecture 6 Chi Square Distributio (χ ) ad Least Squares Fittig Chi Square Distributio (χ ) Suppose: We have a set of measuremets {x 1, x, x }. We kow the true value of each x i (x t1, x t, x t ). We would
More informationFACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING. Lectures
FACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING Lectures MODULE 5 STATISTICS II. Mea ad stadard error of sample data. Biomial distributio. Normal distributio 4. Samplig 5. Cofidece itervals
More informationThe prediction of cement energy demand based on support vector machine Xin Zhang a, *, Shaohong Jing b
4th Iteratioal Coferece o Computer, Mechatroics, Cotrol ad Electroic Egieerig (ICCMCEE 05) The predictio of cemet eergy demad based o support vector machie Xi Zhag a,, Shaohog Jig b School of Electrical
More informationThe Scattering Matrix
2/23/7 The Scatterig Matrix 723 1/13 The Scatterig Matrix At low frequecies, we ca completely characterize a liear device or etwork usig a impedace matrix, which relates the currets ad voltages at each
More informationDirection of Arrival Estimation Method in Underdetermined Condition Zhang Youzhi a, Li Weibo b, Wang Hanli c
4th Iteratioal Coferece o Advaced Materials ad Iformatio Techology Processig (AMITP 06) Directio of Arrival Estimatio Method i Uderdetermied Coditio Zhag Youzhi a, Li eibo b, ag Hali c Naval Aeroautical
More informationClassification of problem & problem solving strategies. classification of time complexities (linear, logarithmic etc)
Classificatio of problem & problem solvig strategies classificatio of time complexities (liear, arithmic etc) Problem subdivisio Divide ad Coquer strategy. Asymptotic otatios, lower boud ad upper boud:
More informationCEE 522 Autumn Uncertainty Concepts for Geotechnical Engineering
CEE 5 Autum 005 Ucertaity Cocepts for Geotechical Egieerig Basic Termiology Set A set is a collectio of (mutually exclusive) objects or evets. The sample space is the (collectively exhaustive) collectio
More informationECE 8527: Introduction to Machine Learning and Pattern Recognition Midterm # 1. Vaishali Amin Fall, 2015
ECE 8527: Itroductio to Machie Learig ad Patter Recogitio Midterm # 1 Vaishali Ami Fall, 2015 tue39624@temple.edu Problem No. 1: Cosider a two-class discrete distributio problem: ω 1 :{[0,0], [2,0], [2,2],
More informationCHAPTER I: Vector Spaces
CHAPTER I: Vector Spaces Sectio 1: Itroductio ad Examples This first chapter is largely a review of topics you probably saw i your liear algebra course. So why cover it? (1) Not everyoe remembers everythig
More informationCSE 1400 Applied Discrete Mathematics Number Theory and Proofs
CSE 1400 Applied Discrete Mathematics Number Theory ad Proofs Departmet of Computer Scieces College of Egieerig Florida Tech Sprig 01 Problems for Number Theory Backgroud Number theory is the brach of
More informationCALCULATION OF FIBONACCI VECTORS
CALCULATION OF FIBONACCI VECTORS Stuart D. Aderso Departmet of Physics, Ithaca College 953 Daby Road, Ithaca NY 14850, USA email: saderso@ithaca.edu ad Dai Novak Departmet of Mathematics, Ithaca College
More informationStudy on Coal Consumption Curve Fitting of the Thermal Power Based on Genetic Algorithm
Joural of ad Eergy Egieerig, 05, 3, 43-437 Published Olie April 05 i SciRes. http://www.scirp.org/joural/jpee http://dx.doi.org/0.436/jpee.05.34058 Study o Coal Cosumptio Curve Fittig of the Thermal Based
More informationDouble Stage Shrinkage Estimator of Two Parameters. Generalized Exponential Distribution
Iteratioal Mathematical Forum, Vol., 3, o. 3, 3-53 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/.9/imf.3.335 Double Stage Shrikage Estimator of Two Parameters Geeralized Expoetial Distributio Alaa M.
More informationFUZZY RELIABILITY ANALYSIS OF COMPOUND SYSTEM BASED ON WEIBULL DISTRIBUTION
IJAMML 3:1 (2015) 31-39 Septeber 2015 ISSN: 2394-2258 Available at http://scietificadvaces.co.i DOI: http://dx.doi.org/10.18642/ijal_7100121530 FUZZY RELIABILITY ANALYSIS OF COMPOUND SYSTEM BASED ON WEIBULL
More information1 Review of Probability & Statistics
1 Review of Probability & Statistics a. I a group of 000 people, it has bee reported that there are: 61 smokers 670 over 5 960 people who imbibe (drik alcohol) 86 smokers who imbibe 90 imbibers over 5
More informationOBJECTIVES. Chapter 1 INTRODUCTION TO INSTRUMENTATION FUNCTION AND ADVANTAGES INTRODUCTION. At the end of this chapter, students should be able to:
OBJECTIVES Chapter 1 INTRODUCTION TO INSTRUMENTATION At the ed of this chapter, studets should be able to: 1. Explai the static ad dyamic characteristics of a istrumet. 2. Calculate ad aalyze the measuremet
More information1.010 Uncertainty in Engineering Fall 2008
MIT OpeCourseWare http://ocw.mit.edu.00 Ucertaity i Egieerig Fall 2008 For iformatio about citig these materials or our Terms of Use, visit: http://ocw.mit.edu.terms. .00 - Brief Notes # 9 Poit ad Iterval
More informationTesting Statistical Hypotheses for Compare. Means with Vague Data
Iteratioal Mathematical Forum 5 o. 3 65-6 Testig Statistical Hypotheses for Compare Meas with Vague Data E. Baloui Jamkhaeh ad A. adi Ghara Departmet of Statistics Islamic Azad iversity Ghaemshahr Brach
More informationPOSSIBILISTIC OPTIMIZATION WITH APPLICATION TO PORTFOLIO SELECTION
THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Series A, OF THE ROMANIAN ACADEMY Volume, Number /, pp 88 9 POSSIBILISTIC OPTIMIZATION WITH APPLICATION TO PORTFOLIO SELECTION Costi-Cipria POPESCU,
More informationQuadratic Functions. Before we start looking at polynomials, we should know some common terminology.
Quadratic Fuctios I this sectio we begi the study of fuctios defied by polyomial expressios. Polyomial ad ratioal fuctios are the most commo fuctios used to model data, ad are used extesively i mathematical
More informationt distribution [34] : used to test a mean against an hypothesized value (H 0 : µ = µ 0 ) or the difference
EXST30 Backgroud material Page From the textbook The Statistical Sleuth Mea [0]: I your text the word mea deotes a populatio mea (µ) while the work average deotes a sample average ( ). Variace [0]: The
More informationMechanical Efficiency of Planetary Gear Trains: An Estimate
Mechaical Efficiecy of Plaetary Gear Trais: A Estimate Dr. A. Sriath Professor, Dept. of Mechaical Egieerig K L Uiversity, A.P, Idia E-mail: sriath_me@klce.ac.i G. Yedukodalu Assistat Professor, Dept.
More informationThe Input-Output Analysis of Construction Industry in West China. Ke Bin Zhang 2, b
Applied Mechaics ad Materials Olie: 214-7-4 ISSN: 1662-7482, Vols. 584-586, pp 2353-2358 doi:1.428/www.scietific.et/amm.584-586.2353 214 ras ech Publicatios, Switzerlad he Iput-Output Aalysis of Costructio
More informationResearch and Application of FAHP in Bidding Quotation for Petroleum Geophysical Prospecting Project
Ope Joural of Statistics, 207, 7, 589-598 http://www.scirp.org/oural/os ISSN Olie: 26-798 ISSN Prit: 26-78X Research ad Applicatio of FAHP i Biddig Quotatio for Petroleum Geophysical Prospectig Proect
More informationPROPOSING INPUT-DEPENDENT MODE CONTRIBUTION FACTORS FOR SIMPLIFIED SEISMIC RESPONSE ANALYSIS OF BUILDING SYSTEMS
he 4 th World Coferece o Earthquake Egieerig October -7, 008, Beiig, Chia PROPOSING INPU-DEPENDEN ODE CONRIBUION FACORS FOR SIPLIFIED SEISIC RESPONSE ANALYSIS OF BUILDING SYSES ahmood Hosseii ad Laya Abbasi
More informationPH 425 Quantum Measurement and Spin Winter SPINS Lab 1
PH 425 Quatum Measuremet ad Spi Witer 23 SPIS Lab Measure the spi projectio S z alog the z-axis This is the experimet that is ready to go whe you start the program, as show below Each atom is measured
More informationIntermittent demand forecasting by using Neural Network with simulated data
Proceedigs of the 011 Iteratioal Coferece o Idustrial Egieerig ad Operatios Maagemet Kuala Lumpur, Malaysia, Jauary 4, 011 Itermittet demad forecastig by usig Neural Network with simulated data Nguye Khoa
More informationADVANCED SOFTWARE ENGINEERING
ADVANCED SOFTWARE ENGINEERING COMP 3705 Exercise Usage-based Testig ad Reliability Versio 1.0-040406 Departmet of Computer Ssciece Sada Narayaappa, Aeliese Adrews Versio 1.1-050405 Departmet of Commuicatio
More informationR is a scalar defined as follows:
Math 8. Notes o Dot Product, Cross Product, Plaes, Area, ad Volumes This lecture focuses primarily o the dot product ad its may applicatios, especially i the measuremet of agles ad scalar projectio ad
More informationProduct Mix Problem with Radom Return and Preference of Production Quantity. Osaka University Japan
Product Mix Problem with Radom Retur ad Preferece of Productio Quatity Hiroaki Ishii Osaka Uiversity Japa We call such fiace or idustrial assets allocatio problems portfolio selectio problems, ad various
More informationEE260: Digital Design, Spring n MUX Gate n Rudimentary functions n Binary Decoders. n Binary Encoders n Priority Encoders
EE260: Digital Desig, Sprig 2018 EE 260: Itroductio to Digital Desig MUXs, Ecoders, Decoders Yao Zheg Departmet of Electrical Egieerig Uiversity of Hawaiʻi at Māoa Overview of Ecoder ad Decoder MUX Gate
More informationStatistics 511 Additional Materials
Cofidece Itervals o mu Statistics 511 Additioal Materials This topic officially moves us from probability to statistics. We begi to discuss makig ifereces about the populatio. Oe way to differetiate probability
More informationANOTHER GENERALIZED FIBONACCI SEQUENCE 1. INTRODUCTION
ANOTHER GENERALIZED FIBONACCI SEQUENCE MARCELLUS E. WADDILL A N D LOUIS SACKS Wake Forest College, Wisto Salem, N. C., ad Uiversity of ittsburgh, ittsburgh, a. 1. INTRODUCTION Recet issues of umerous periodicals
More informationAdvanced Analysis. Min Yan Department of Mathematics Hong Kong University of Science and Technology
Advaced Aalysis Mi Ya Departmet of Mathematics Hog Kog Uiversity of Sciece ad Techology September 3, 009 Cotets Limit ad Cotiuity 7 Limit of Sequece 8 Defiitio 8 Property 3 3 Ifiity ad Ifiitesimal 8 4
More informationLecture 6 Chi Square Distribution (χ 2 ) and Least Squares Fitting
Lecture 6 Chi Square Distributio (χ ) ad Least Squares Fittig Chi Square Distributio (χ ) Suppose: We have a set of measuremets {x 1, x, x }. We kow the true value of each x i (x t1, x t, x t ). We would
More informationECON 3150/4150, Spring term Lecture 3
Itroductio Fidig the best fit by regressio Residuals ad R-sq Regressio ad causality Summary ad ext step ECON 3150/4150, Sprig term 2014. Lecture 3 Ragar Nymoe Uiversity of Oslo 21 Jauary 2014 1 / 30 Itroductio
More informationComparison of the COG Defuzzification Technique and Its Variations to the GPA Index
Compariso of the COG Defuzzificatio Techique ad Its Variatios to the GPA Idex Michael Gr. Voskoglou Departmet of Mathematical Scieces, School of Techological Applicatios Graduate Techological Educatioal
More informationStructural Functionality as a Fundamental Property of Boolean Algebra and Base for Its Real-Valued Realizations
Structural Fuctioality as a Fudametal Property of Boolea Algebra ad Base for Its Real-Valued Realizatios Draga G. Radojević Uiversity of Belgrade, Istitute Mihajlo Pupi, Belgrade draga.radojevic@pupi.rs
More informationTHE SYSTEMATIC AND THE RANDOM. ERRORS - DUE TO ELEMENT TOLERANCES OF ELECTRICAL NETWORKS
R775 Philips Res. Repts 26,414-423, 1971' THE SYSTEMATIC AND THE RANDOM. ERRORS - DUE TO ELEMENT TOLERANCES OF ELECTRICAL NETWORKS by H. W. HANNEMAN Abstract Usig the law of propagatio of errors, approximated
More informationChapter 6 Sampling Distributions
Chapter 6 Samplig Distributios 1 I most experimets, we have more tha oe measuremet for ay give variable, each measuremet beig associated with oe radomly selected a member of a populatio. Hece we eed to
More informationAn Intuitionistic fuzzy count and cardinality of Intuitionistic fuzzy sets
Malaya Joural of Matematik 4(1)(2013) 123 133 A Ituitioistic fuzzy cout ad cardiality of Ituitioistic fuzzy sets B. K. Tripathy a, S. P. Jea b ad S. K. Ghosh c, a School of Computig Scieces ad Egieerig,
More informationPAijpam.eu ON DERIVATION OF RATIONAL SOLUTIONS OF BABBAGE S FUNCTIONAL EQUATION
Iteratioal Joural of Pure ad Applied Mathematics Volume 94 No. 204, 9-20 ISSN: 3-8080 (prited versio); ISSN: 34-3395 (o-lie versio) url: http://www.ijpam.eu doi: http://dx.doi.org/0.2732/ijpam.v94i.2 PAijpam.eu
More informationAlgebra of Least Squares
October 19, 2018 Algebra of Least Squares Geometry of Least Squares Recall that out data is like a table [Y X] where Y collects observatios o the depedet variable Y ad X collects observatios o the k-dimesioal
More informationApplication Bayesian Approach in Tasks Decision-Making Support
America Joural of Applied Mathematics ad Statistics, 05, Vol 3, No 6, 57-6 Available olie at http://pubssciepubcom/ajams/3/6/7 Sciece ad Educatio Publishig DOI:069/ajams-3-6-7 Applicatio Bayesia Approach
More information3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense,
3. Z Trasform Referece: Etire Chapter 3 of text. Recall that the Fourier trasform (FT) of a DT sigal x [ ] is ω ( ) [ ] X e = j jω k = xe I order for the FT to exist i the fiite magitude sese, S = x [
More informationComparison of Methods for Estimation of Sample Sizes under the Weibull Distribution
Iteratioal Joural of Applied Egieerig Research ISSN 0973-4562 Volume 12, Number 24 (2017) pp. 14273-14278 Research Idia Publicatios. http://www.ripublicatio.com Compariso of Methods for Estimatio of Sample
More informationMeasurement uncertainty of the sound absorption
Measuremet ucertaity of the soud absorptio coefficiet Aa Izewska Buildig Research Istitute, Filtrowa Str., 00-6 Warsaw, Polad a.izewska@itb.pl 6887 The stadard ISO/IEC 705:005 o the competece of testig
More informationTEACHER CERTIFICATION STUDY GUIDE
COMPETENCY 1. ALGEBRA SKILL 1.1 1.1a. ALGEBRAIC STRUCTURES Kow why the real ad complex umbers are each a field, ad that particular rigs are ot fields (e.g., itegers, polyomial rigs, matrix rigs) Algebra
More informationRun-length & Entropy Coding. Redundancy Removal. Sampling. Quantization. Perform inverse operations at the receiver EEE
Geeral e Image Coder Structure Motio Video (s 1,s 2,t) or (s 1,s 2 ) Natural Image Samplig A form of data compressio; usually lossless, but ca be lossy Redudacy Removal Lossless compressio: predictive
More informationExpert System of Fault Diagnosis for Gear Box in Wind Turbine
Available olie at www.sciecedirect.com Systems Egieerig Procedia 4 (202) 89 95 The 2 d Iteratioal Coferece o Complexity Sciece & Iformatio Egieerig Expert System of Fault Diagosis for Gear Box i Wid Turbie
More informationOn Distance and Similarity Measures of Intuitionistic Fuzzy Multi Set
IOSR Joural of Mathematics (IOSR-JM) e-issn: 78-578. Volume 5, Issue 4 (Ja. - Feb. 03), PP 9-3 www.iosrourals.org O Distace ad Similarity Measures of Ituitioistic Fuzzy Multi Set *P. Raaraeswari, **N.
More informationInternational Journal of Performability Engineering, Vol. 1, No. 1, July 2005, pp RAMS Consultants Printed in India
Iteratioal Joural of Performability Egieerig, Vol. 1, No. 1, July 2005, pp. 23-36 RAMS Cosultats Prited i Idia LIYANG XIE 1, JINYU ZHOU 1, YONGYAN WANG 2, XUEMIN WANG 1 1 Northeaster Uiversity, Sheyag,
More informationRecursive Algorithms. Recurrences. Recursive Algorithms Analysis
Recursive Algorithms Recurreces Computer Sciece & Egieerig 35: Discrete Mathematics Christopher M Bourke cbourke@cseuledu A recursive algorithm is oe i which objects are defied i terms of other objects
More informationEnterprise interoperability measurement - Basic concepts
Eterprise iteroperability measuremet - Basic cocepts Nicolas Dacli, David Che, Bruo Vallespir LAPS/GRAI, Uiversity Bordeaux 1, ENSEIRB, UMR 5131 CNRS, 351 cours de la Libératio, 33405 Talece Cedex, Frace
More informationOutput Analysis (2, Chapters 10 &11 Law)
B. Maddah ENMG 6 Simulatio Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should be doe
More informationCHAPTER 10 INFINITE SEQUENCES AND SERIES
CHAPTER 10 INFINITE SEQUENCES AND SERIES 10.1 Sequeces 10.2 Ifiite Series 10.3 The Itegral Tests 10.4 Compariso Tests 10.5 The Ratio ad Root Tests 10.6 Alteratig Series: Absolute ad Coditioal Covergece
More informationECONOMIC OPERATION OF POWER SYSTEMS
ECOOMC OEATO OF OWE SYSTEMS TOUCTO Oe of the earliest applicatios of o-lie cetralized cotrol was to provide a cetral facility, to operate ecoomically, several geeratig plats supplyig the loads of the system.
More informationPerformance of Stirling Engines * (Arranging Method of Experimental Results and Performance Prediction) Abstract. 1. Introduction
1 Performace of Stirlig Egies (Arragig Method of Experimetal Results ad Performace Predictio) Shoichi IWAMOTO Koichi HIRATA ad Fujio TODA Key Words: Stirlig Egie, Heat Exchager, Frictio, Egie Desig, Mechaical
More informationGROUND MOTION OF NON-CIRCULAR ALLUVIAL VALLEY FOR INCIDENT PLANE SH-WAVE. Hui QI, Yong SHI, Jingfu NAN
The th World Coferece o Earthquake Egieerig October -7, 8, Beiig, Chia GROUND MOTION OF NON-CIRCULAR ALLUVIAL VALLEY FOR INCIDENT PLANE SH-WAVE Hui QI, Yog SHI, Jigfu NAN ABSTRACT : Professor, Dept. of
More informationEvapotranspiration Estimation Using Support Vector Machines and Hargreaves-Samani Equation for St. Johns, FL, USA
Evirometal Egieerig 0th Iteratioal Coferece eissn 2029-7092 / eisbn 978-609-476-044-0 Vilius Gedimias Techical Uiversity Lithuaia, 27 28 April 207 Article ID: eviro.207.094 http://eviro.vgtu.lt DOI: https://doi.org/0.3846/eviro.207.094
More informationFilter banks. Separately, the lowpass and highpass filters are not invertible. removes the highest frequency 1/ 2and
Filter bas Separately, the lowpass ad highpass filters are ot ivertible T removes the highest frequecy / ad removes the lowest frequecy Together these filters separate the sigal ito low-frequecy ad high-frequecy
More informationDiscrete Orthogonal Moment Features Using Chebyshev Polynomials
Discrete Orthogoal Momet Features Usig Chebyshev Polyomials R. Mukuda, 1 S.H.Og ad P.A. Lee 3 1 Faculty of Iformatio Sciece ad Techology, Multimedia Uiversity 75450 Malacca, Malaysia. Istitute of Mathematical
More informationMechatronics. Time Response & Frequency Response 2 nd -Order Dynamic System 2-Pole, Low-Pass, Active Filter
Time Respose & Frequecy Respose d -Order Dyamic System -Pole, Low-Pass, Active Filter R 4 R 7 C 5 e i R 1 C R 3 - + R 6 - + e out Assigmet: Perform a Complete Dyamic System Ivestigatio of the Two-Pole,
More informationSCALING OF NUMBERS IN RESIDUE ARITHMETIC WITH THE FLEXIBLE SELECTION OF SCALING FACTOR
POZNAN UNIVE RSITY OF TE CHNOLOGY ACADE MIC JOURNALS No 76 Electrical Egieerig 203 Zeo ULMAN* Macie CZYŻAK* Robert SMYK* SCALING OF NUMBERS IN RESIDUE ARITHMETIC WITH THE FLEXIBLE SELECTION OF SCALING
More information577. Estimation of surface roughness using high frequency vibrations
577. Estimatio of surface roughess usig high frequecy vibratios V. Augutis, M. Sauoris, Kauas Uiversity of Techology Electroics ad Measuremets Systems Departmet Studetu str. 5-443, LT-5368 Kauas, Lithuaia
More informationPAijpam.eu ON TENSOR PRODUCT DECOMPOSITION
Iteratioal Joural of Pure ad Applied Mathematics Volume 103 No 3 2015, 537-545 ISSN: 1311-8080 (prited versio); ISSN: 1314-3395 (o-lie versio) url: http://wwwijpameu doi: http://dxdoiorg/1012732/ijpamv103i314
More informationAn Improved RAHP/DEA Method and the Application of the Physical Education Teaching Quality Assessment
, pp.53-64 http://dx.doi.org/0.457/iuesst.05.8.3.05 A Improved RAHP/DEA Method ad the Applicatio of the Physical Educatio eachig Quality Assessmet Hao Li ad ie Ru Health scieces of Xi a physical educatio
More informationLinear time invariant systems
Liear time ivariat systems Alejadro Ribeiro Dept. of Electrical ad Systems Egieerig Uiversity of Pesylvaia aribeiro@seas.upe.edu http://www.seas.upe.edu/users/~aribeiro/ February 25, 2016 Sigal ad Iformatio
More information