NON-LINEAR MODELLING OF A GEOTHERMAL STEAM PIPE
|
|
- Charlene James
- 5 years ago
- Views:
Transcription
1 14thNew Zealad Workshop 1992 NON-LNEAR MODELLNG OF A GEOTHERMAL STEAM PPE Y. Huag ad D. H. Freesto Geothermal stitute, Uiversity of Aucklad SUMMARY Recet work o developig a o-liear model for a geothermal pipe etwork system is preseted i this paper. Previous methods of modellig are reviewed. Usig the mass ad eergy balace at each ode ad loop of a pipe etwork, a o-liear equatio set ca be established. The equatio set is formulated from a coceptual model of the pipe etwork, which is composed of steam wells ad coected pipelies. The well characteristics curves, pipelie frictioal characteristic ad the differet combiatios of the coected compoets all cotribute to the pressure ad mass flow rate distributios i the system. Some recet umerical experimets o the o-liear model are compared with talia experiece. The results coverged satisfactorily. Usig this model, the user ca chage the coectio ad the characteristic of each idividual demad i a etwork ad chose a desired maifold pressure; the simulator will the calculate the balaced mass flow rate ad pressure distributio alog the defied pipe etwork. 1 NTRODUCTON Computer modellig of geothermal pipe etworks for both desig ad simulatio purposes has bee reported. Most of these are liear computig models, which ca work well o a tree-like liked simple pipe etwork. However with more complex practical systems, it is easy to fid that both loops of pipelies ad a series of oliear well characteristics have to be cosidered. These two factors cotribute to the difficulty of the modellig work. Loops i a pipe etwork ca ormally be solved usig a umber of established methods (Stepheso, 1989). However if the pipe etwork is coected to a umber of wells with parabolic like characteristic curves rather tha liear curves, eve the calculatio of a simple etwork ca be a cumbersome process. Covergece of the solutio is ofte very slow because of the trial ad error methods used. This paper presets recet developmet work o a umerical model which uses a o-liear method to simulate a geothermal steam pipelie etwork. The mass ad pressure balace at each ode ad loop of a pipe etwork are cosidered to be uder the cotrol of both the coected well ad the maifold workig poit. After settig up a o-liear equatio set for the above balace, umerical methods are used to solve for the mass flow ad pressure distributio. Covergece of the solutio has bee satisfactory for the umerical experimets coducted. this paper, a recet simulatio o oe of the logest etworks at Larderello, taly, is preseted. The simulatio results are compared with field measuremets ad a earlier simulatio by Marcocii ad Neri (1979). Sesitivity of the simulatio to the pipelie loss factor ad well characteristics are discussed. Sice the o-liear model solves the set of equatios describig a etwork simultaeously, it has good flexibility, makig it particularly applicable to looped etworks which are much more difficult to solve tha a tree-like etwork. 2 NON-LNEAR MODELLNG STRATEGY A o-liear model solves the equatio set simultaeously usig a umerical method formulated from the coceptual model of the pipe etwork. A computer code has bee developed based o this o-liear modellig strategy. The simulatio results for a series of test models have show a satisfactory covergece of the solutio. 2.1 Review The pressure ad mass flow rate distributio through a pipe etwork are geerally cotrolled by the pressure differece betwee the iput ad output poits of the system. a steady-state operatio, the mass flow ad pressure drop at each ode ad loop should be balaced that is: the et flow towards ayjuctio or odes is ZERO, ad the et head loss aroud ay closed loop is ZERO. Head loss alog a pipe lie are usually assumed to be of the form Ah= where Ah is the head loss, k the factor, L is the pipe legth, Q the volume flow rate ad D the iteral diameter of the pipe. Most methods of etwork aalysis are based o the above equatio (Stepheso, 1989). Two early approachs to pipe etwork aalysis were the Loop Flow Correctio Method ad the Node Head Correctio Method. Both methods use successive correctors speeded by a mathematical techique developed by Hardy Cross (1936). The developmet of micro computers has made it much easier to perform a etwork aalysis by umerical methods. This ivolves the simultaeous solutio of equatios describig flow ad pressure balace. Whe the iputs to a etwork system are steam wells with parabolic characteristics, a oliear umerical solutio is a requiremet of the model.
2 No-liear Modellig A coceptual model which ca represet the real pipe etwork is the fust requiremet for settig up a o-liear equatio set. A effective umerical method is ecessary for a accurate solutio with quick covergece Coceptual Model Before pressure ad mass balaces are applied at each loop ad ode, a coceptual model is required. This model should reflect all the iterrelatios betwee each part of the etwork ad should be cocise ad easy to use. Fig. 1 shows a typical coceptual model of a etwork where ad idicate the characteristic curves of the three steam wells, idicates the required steam pressure at the maifold,,, ad are the stable-state mass flows i the etwork, ad the odes are umbered as 1, 2, 3, 4, 5 ad 6. Dummy lies, represeted by dashed lie are used betwee each iput ad output poit of the system. With the help of these dummy lies, the etwork is liked by a umber of eclosed loops o which the pressure balace rule of a loop ca be applied. The expected flow directios are marked o each pipelie. The followig covetios are the applied to establish a equatio set for the etwork. At a balaced ode the iput flow is positive, output flow is egative. a balaced loop, a arbitrary calculatio directio of the loop is assumed. f a well output has a same directio as tlie calculatio directio the well head pressure is positive, otherwise it is egative; the opposite rule is applied for output pressure i steam maifold. f a pipe flow has a same directio as the calculatio directio, tlie frictioal pressure drop is positive. otherwise it is egative. tlie dummy pipe, the mass flow rate is defied as zero Establishig the equatio the coceptual model of Fig. 1, well head pressure ca be expressed as: + + where A, B ad C are regressio coefficiets of the well characteristic curve ad m is mass flow of the well. Frictioal pressure loss alog the pipelies is give as: where K is the loss factor o a sectio of a pipelie. A system costrait is the requiremet of a fixed output pressure at ode 6, so the mass ad pressure balace equatio set ca be writte as: - - = = = = From equatio (1) ad (2) it is obvious that the equatio set (3) is a o-liear set ad should have a simultaeous solutio for, ad,if they exist. Numerical Solutio For a oliear equatio set such as i = 1, 2, We ca defie a objective fuctio 6 m 50 m 50m m Fig. 1 A typical cocept model of a etwork i Whe we have the set (4). 1 are roots of the oliear equatio Programmig for the above process is performed as follows: Startig from a iitial guess of o-zero roots suppose tlie iteratio has progressed to the step, the we have 2. Calculate the objective fuctio
3 f c E, the is take as a solutio, otherwise go to ext step; 4. Calculate: well 1 well 3 where or take c = 5. Calculate: i = 1, 2, Fig. 2 Basic test model j=l the repeat from step 2 util covergece is obtaied at step 3. A computer code, writte i TURBO PASCAL, for the solutio process has bee developed (Huag, 1991). 2.3 Test Model order to test the computer program, well data from the geothermal field has bee used i a test model. The operatio of the program ad the iterrelatios betwee parameters (Huag, 1992) have bee ivestigated. Differet coectios, usig the same basic model were simulated i order to compare results for differet operatio coditios. Test Network The basic model is show i Fig. 2. The model is composed of four productio wells, a sigle-looped brach lie etwork betwee the wells, ad a mai lie coectig the etwork to a power house (steam cosumer). With this model, it is show how a oliear looped etwork is solved, although such coectios may ot be ecessary i practice. the layout of the coceptual model of this etwork, m2, m3, ad represet the steam mass flow from wells 1, well 2, well 3 ad well 4 respectively. All these mass flows are cotrolled by the well ad separator characteristics ad However, the frictioal pressure loss alog each lie also make a cotributio to the cotrol of all the mass flow rates from to mg. This frictioal pressure loss is described by = The frictio loss factor is defied as: 32 f where f is Faig frictio factor (Perry, R. H., ad D are the pipe legth ad iside diameter, ad desity of the steam. is the The turbie ilet steam pressure is set at = 13.5 bara.. The pipe etwork has ie ukow variables, to ad ie oliear equatios ca be established. A costat value is used for this test model Test Model Results Usig the model described above, a series of test rus were made with differet combiatios of the workig wells used to simulate the possible differet workig coditios. Each combiatio followed the law that if oe well is shut off, the correspodig likig brach lies are also shut off. All the simulatios coverged satisfactorily. Results are show i Table 1. The etwork output steam is used as the iput for Turbie ad the system output is give i terms of Turbie output i MW. This umerical experimet o the o-liear model illustrates that a pipe etwork ca be simulated for ay combiatio of wells o-lie ad differet pipe frictioal characteristics.
4 Table 1 System performace with differet wells o-lie Well MAN D TURBONE t Fig. 3 A steam pipe etwork layout Note: RMFC - Relative Mass Flow Cotributio The results of these simulatios ca be used to predict the geeral performace of a o-liear pipe etwork system whe (a) the umber ad order of the wells o-lie have bee chaged (some wells shut off); (b) the frictioal characteristics of ay pipelie have bee chaged (valvig); the characteristic curve of ay productio well chages due to log term operatio. 3. SMULATON OF A STEAM PPE NETWORK The o-liear model was applied o oe of the logest steam pipe etworks operatig at Larderello, taly ad the results compared to published data. The coceptual model of the etwork ad the simulatio results are preseted. 11 Maifold Productiowells 1 8 ' 7 6 8' 7' 4' 3.1 Network Layout ad Coceptual Model This etwork carries fluid from 1, Querciola 2, Capriola, Grottitaa ad VC 2 wells to the Serrazzao power plat. Fig. 3 illustrates the layout of the pipe system. Several codesate dischargers are placed alog tlie lie. The characteristic curves of the differet wells were calculated from published data. The loss factor, K, is based o the geometry of each pipelie ad the correspodig steam state. A coceptual model for the etwork is show i Fig. 4 Coceptual model
5 Results A o-liear umerical simulatio of the Larderello pipelie etwork was successfully performed with three differet sets of iput data i TEST 4, TEST 5 ad TEST 6. The iterative procedure takes about 5 CPU miutes to coverge o a BM 386 computer. The results were prited as the mass flow rate from to The required maifold pressure was take from published data (Marcocii ad Neri, 1979). TEST 5, the K value for pipelies betwee well Capriola ad VC 2 has bee modified by a icrease show as follows TEST TEST K TEST 6, a costat Faig frictio factor which is a average value for geothermal pipig (Huag, was used i the calculatio of all the K values throughout the etwork. The mass flow rate for each well from the results is used i the well characteristic curves to give the operatig wellhead pressures. Pressure profiles are the plotted over the measured data alog the pipelie etwork, as show i Fig. 5. The resultat curves represetig TEST 4, TEST 5 ad TEST 6 fall withi a close rage of the measured data irrespective of the differece i iput data. Cosiderig the simplificatio made, the result is good eough to show a agreemet betwee the umerical simulatio ad the measuremets. 4. DSCUSSON Oe of the sesitive parameters i the simulatio is the loss factor K. mproperly used K values i the system may lead to a o-coverget simulatio. Fortuately, K value foud i practice is depedet o the chage of Faig frictio factor f, which happes to fall i a arrow rage. Differet tests have show that the simulatio results for pressure drop are ot too sesitive to Faig frictio factor f. the compariso betwee the simulatio ad measuremet is illustrated. The arrow gap betwee the two measuremets may idicate measuremet errors. Most of the simulatio results fall withi the rage of measuremet error, which idicate a good agreemet with measuremet. All three simulatios, TEST 4, TEST 5 ad TEST 6 have a slightly flatter pressure profile alog the pipelie tha the measured data. This is because localized frictioal loss has bee eglected o the simulatio at this stage. For the results for TEST 4, the pressure profile has a similar slope to the measuremets except for the pipelies from ode 4 to 8. This might be due to some additio localized frictioal loss. TEST 5, the K value for all pipelies has bee modified by a small icrease. The simulatio result shows that the slope of the pressure profile betwee ode 4 ad 8 is closer to the measured oe, demostratig the sesitivity to the K value. TEST 6 is based o a costat Faig frictio factor f of The objective of this test was to ivestigate the sesitivity to f. t is iterestig to ote that the resultat pressure profile of this test is very close to that of TEST 4. This is a idicatio that the f value, if withi a resoable rage, is ot a sesitive parameter i this umerical simulatio. Amog the variables ivolved i evaluatig K, pipe diameter is the most sesitive oe for estimatig pressure drop. Fortuately it is oe of most well specified parameters. Of the mai parameters, productio well characteristic curves are of special importace. These cotrol the geeral performace of a coected pipelie etwork, though the chage of the frictioal characteristic of the etwork ca brig a chage i the geeral performace to some extet. t is the well curve which cotrols how much mass flow the well cotributes to the etwork. Sice each well may have its ow characteristic curve, ay pressure chage alog pipelie ca cause a correspodig chage of the workig poit of the well alog its productio curve. As a result, the well productio rate is chaged which the leads to a cosequet chage i pressure drop o the etwork. Needless to say, this ca also brig a ifluece o the workig poits of other wells ad their productio rates Simulatio TEST4 Simulatio TEST5 Simulatio Measuremet-1 Measuremet-2 TEST6 VAPSTAT a Progressive distace Fig. 5 Results compared with measuremets Progressive distace Fig. 6 compared with other simulatio
6 110 The ifluece o the other well operatig poits of chagig a well characteristic curve is very complex. t is a fuctio of their curve shape, the frictioal characteristic of each pipelie ad the mass ad eergy balace of the whole etwork. some cases, it ca cause a icrease i the total system output while i some other opposite effect occurs. Geerally speakig, a cluster of wells havig similar characteristic curves ted to give a simpler etwork which is easy to cotrol. With the help of the simulatio, well head cotrol of the workig poit ca be used as a systematic cotrol to a pipe etwork, especially after there has bee a chage to the etwork system. To examie more detailed iterrelatios betwee wells, a study of differet combiatios of wells ad the correspodig simulatio results are eeded. At this stage, the calculatio i the mathematical model is based o saturated steam. Heat loss alog the pipelie has ot yet bee take ito accout. The results from simulatio TEST 6 have show little differece from the published results of a other simulatio VAPSTAT 1 (Marcocii ad Neri, 1979) as illustrated i Fig. 6. The similarity of the two simulatio results idicates that the superheat of the steam ad the heat loss alog the pipelie play little part i the umerical simulatio. VAPSTAT 1 about 80 C superheat of the steam is cosidered. Heat losses through the pipelie surface are also icluded. From steam tables, it ca be see that 80 C super-heatig causes a 18% chage i desity of steam at a pressure of 8 This small chage seems to cause very little chage to the f value ad the cosequet pressure drop. Sice the pipelie is isulated, the temperature drop alog the pipelie is small. This small reductio of the superheat has little effect o the pressure drop. 5. CONCLUSONS 1. A o-liear model for the umerical simulatio of a geothermal steam pipe etwork has bee developed. A mass flow ad pressure balace at each ode ad loop i the etwork is used to establish a o-liear equatio set. Well characteristic curves ormally domiate the distributio of the mass flow withi a pipe etwork ad total output. alog the pipelie is caused by eglectig the localized frictioal loss. 3. Differet simulatio results have show that they are ot sesitive to the Faig frictio factor This may idicate the possibility of usig a costat or liear (agaist pipe roughess f value for a simplified calculatio of pressure drop. The correlatio used for frictioal pressure drop is proportioal to the pipe diameter to the mius fifth power, the diameter D becomes the most sesitive factor i the calculatio. 4. With the o-liear model, the simulatio of a pipelie etwork ca be applied ot oly to a tree-like system, as for VAPSTAT 1, but also to a looped oe. The o-liear model allows chages of coditios i the etwork system ad chages to the maifold pressure to be made at the discretio of the user. 6. ACKNOWLEDGEMENTS The authors would like to ackowledge Desigpower New Zealad limited for the fiacial support ad their special advice to this research project. 7. REFERENCES Cross, H. (1936): Aalysis of flow i etworks of codiuts or coductors, Uiversity of lliois Bulleti, 286 Huag, Y.C. (1991): Computer Modellig o A Multipump-statio Geothermal Pipe Network System (Part A), Research Report (4) to Desigpower, 1991, Huag, Y.C. (1992): Computer Modellig o A Multipump-statio Geothermal Pipe Network System (Part B): A Numerical Experimet, Research Report (5) to Desigpower, March 1992, pp. 39 Marcocii, R. ad Neri, G. (1979): Numerical Simulatio of a Steam Pipelie Network, Geothermics, Vol. 7 pp , With the successful umerical simulatio of oe Perry, R.H. ad Gree, D.M. (1987): Perry's Chemical logest steam pipe etwork i Larderello, the oliear model has bee validated. Superheatig of the egieerig series. Egieers' Hadbook, McGraw-Hill chemical steam ad the heat loss through pipelie surface are ot calculated at this Stage. The coverged, With results close to the measured data withi 5 miutes CPU Elsevier Sciece Publishers B. V., The time. The flatter slope of the simulated pressure profile Netherlads
Civil Engineering Computation
Civil Egieerig Computatio Fidig Roots of No-Liear Equatios March 14, 1945 World War II The R.A.F. first operatioal use of the Grad Slam bomb, Bielefeld, Germay. Cotets 2 Root basics Excel solver Newto-Raphso
More informationPattern Recognition Systems Lab 1 Least Mean Squares
Patter Recogitio Systems Lab 1 Least Mea Squares 1. Objectives This laboratory work itroduces the OpeCV-based framework used throughout the course. I this assigmet a lie is fitted to a set of poits usig
More information. Written in factored form it is easy to see that the roots are 2, 2, i,
CMPS A Itroductio to Programmig Programmig Assigmet 4 I this assigmet you will write a java program that determies the real roots of a polyomial that lie withi a specified rage. Recall that the roots (or
More informationSection 7.2: Direction Fields and Euler s Methods
Sectio 7.: Directio ields ad Euler s Methods Practice HW from Stewart Tetbook ot to had i p. 5 # -3 9-3 odd or a give differetial equatio we wat to look at was to fid its solutio. I this chapter we will
More informationOnes Assignment Method for Solving Traveling Salesman Problem
Joural of mathematics ad computer sciece 0 (0), 58-65 Oes Assigmet Method for Solvig Travelig Salesma Problem Hadi Basirzadeh Departmet of Mathematics, Shahid Chamra Uiversity, Ahvaz, Ira Article history:
More informationBezier curves. Figure 2 shows cubic Bezier curves for various control points. In a Bezier curve, only
Edited: Yeh-Liag Hsu (998--; recommeded: Yeh-Liag Hsu (--9; last updated: Yeh-Liag Hsu (9--7. Note: This is the course material for ME55 Geometric modelig ad computer graphics, Yua Ze Uiversity. art of
More informationLecture 18. Optimization in n dimensions
Lecture 8 Optimizatio i dimesios Itroductio We ow cosider the problem of miimizig a sigle scalar fuctio of variables, f x, where x=[ x, x,, x ]T. The D case ca be visualized as fidig the lowest poit of
More informationOCR Statistics 1. Working with data. Section 3: Measures of spread
Notes ad Eamples OCR Statistics 1 Workig with data Sectio 3: Measures of spread Just as there are several differet measures of cetral tedec (averages), there are a variet of statistical measures of spread.
More informationPolynomial Functions and Models. Learning Objectives. Polynomials. P (x) = a n x n + a n 1 x n a 1 x + a 0, a n 0
Polyomial Fuctios ad Models 1 Learig Objectives 1. Idetify polyomial fuctios ad their degree 2. Graph polyomial fuctios usig trasformatios 3. Idetify the real zeros of a polyomial fuctio ad their multiplicity
More informationThe Closest Line to a Data Set in the Plane. David Gurney Southeastern Louisiana University Hammond, Louisiana
The Closest Lie to a Data Set i the Plae David Gurey Southeaster Louisiaa Uiversity Hammod, Louisiaa ABSTRACT This paper looks at three differet measures of distace betwee a lie ad a data set i the plae:
More informationAnalysis Metrics. Intro to Algorithm Analysis. Slides. 12. Alg Analysis. 12. Alg Analysis
Itro to Algorithm Aalysis Aalysis Metrics Slides. Table of Cotets. Aalysis Metrics 3. Exact Aalysis Rules 4. Simple Summatio 5. Summatio Formulas 6. Order of Magitude 7. Big-O otatio 8. Big-O Theorems
More informationAlpha Individual Solutions MAΘ National Convention 2013
Alpha Idividual Solutios MAΘ Natioal Covetio 0 Aswers:. D. A. C 4. D 5. C 6. B 7. A 8. C 9. D 0. B. B. A. D 4. C 5. A 6. C 7. B 8. A 9. A 0. C. E. B. D 4. C 5. A 6. D 7. B 8. C 9. D 0. B TB. 570 TB. 5
More informationPerformance Plus Software Parameter Definitions
Performace Plus+ Software Parameter Defiitios/ Performace Plus Software Parameter Defiitios Chapma Techical Note-TG-5 paramete.doc ev-0-03 Performace Plus+ Software Parameter Defiitios/2 Backgroud ad Defiitios
More informationCS 683: Advanced Design and Analysis of Algorithms
CS 683: Advaced Desig ad Aalysis of Algorithms Lecture 6, February 1, 2008 Lecturer: Joh Hopcroft Scribes: Shaomei Wu, Etha Feldma February 7, 2008 1 Threshold for k CNF Satisfiability I the previous lecture,
More informationHow do we evaluate algorithms?
F2 Readig referece: chapter 2 + slides Algorithm complexity Big O ad big Ω To calculate ruig time Aalysis of recursive Algorithms Next time: Litterature: slides mostly The first Algorithm desig methods:
More informationImprovement of the Orthogonal Code Convolution Capabilities Using FPGA Implementation
Improvemet of the Orthogoal Code Covolutio Capabilities Usig FPGA Implemetatio Naima Kaabouch, Member, IEEE, Apara Dhirde, Member, IEEE, Saleh Faruque, Member, IEEE Departmet of Electrical Egieerig, Uiversity
More informationBayesian approach to reliability modelling for a probability of failure on demand parameter
Bayesia approach to reliability modellig for a probability of failure o demad parameter BÖRCSÖK J., SCHAEFER S. Departmet of Computer Architecture ad System Programmig Uiversity Kassel, Wilhelmshöher Allee
More informationRedundancy Allocation for Series Parallel Systems with Multiple Constraints and Sensitivity Analysis
IOSR Joural of Egieerig Redudacy Allocatio for Series Parallel Systems with Multiple Costraits ad Sesitivity Aalysis S. V. Suresh Babu, D.Maheswar 2, G. Ragaath 3 Y.Viaya Kumar d G.Sakaraiah e (Mechaical
More informationAn Improved Shuffled Frog-Leaping Algorithm for Knapsack Problem
A Improved Shuffled Frog-Leapig Algorithm for Kapsack Problem Zhoufag Li, Ya Zhou, ad Peg Cheg School of Iformatio Sciece ad Egieerig Hea Uiversity of Techology ZhegZhou, Chia lzhf1978@126.com Abstract.
More informationImproving Template Based Spike Detection
Improvig Template Based Spike Detectio Kirk Smith, Member - IEEE Portlad State Uiversity petra@ee.pdx.edu Abstract Template matchig algorithms like SSE, Covolutio ad Maximum Likelihood are well kow for
More informationEM375 STATISTICS AND MEASUREMENT UNCERTAINTY LEAST SQUARES LINEAR REGRESSION ANALYSIS
EM375 STATISTICS AND MEASUREMENT UNCERTAINTY LEAST SQUARES LINEAR REGRESSION ANALYSIS I this uit of the course we ivestigate fittig a straight lie to measured (x, y) data pairs. The equatio we wat to fit
More informationLecturers: Sanjam Garg and Prasad Raghavendra Feb 21, Midterm 1 Solutions
U.C. Berkeley CS170 : Algorithms Midterm 1 Solutios Lecturers: Sajam Garg ad Prasad Raghavedra Feb 1, 017 Midterm 1 Solutios 1. (4 poits) For the directed graph below, fid all the strogly coected compoets
More informationMATHEMATICAL METHODS OF ANALYSIS AND EXPERIMENTAL DATA PROCESSING (Or Methods of Curve Fitting)
MATHEMATICAL METHODS OF ANALYSIS AND EXPERIMENTAL DATA PROCESSING (Or Methods of Curve Fittig) I this chapter, we will eamie some methods of aalysis ad data processig; data obtaied as a result of a give
More informationUsing the Keyboard. Using the Wireless Keyboard. > Using the Keyboard
1 A wireless keyboard is supplied with your computer. The wireless keyboard uses a stadard key arragemet with additioal keys that perform specific fuctios. Usig the Wireless Keyboard Two AA alkalie batteries
More informationNumerical Methods Lecture 6 - Curve Fitting Techniques
Numerical Methods Lecture 6 - Curve Fittig Techiques Topics motivatio iterpolatio liear regressio higher order polyomial form expoetial form Curve fittig - motivatio For root fidig, we used a give fuctio
More informationA Resource for Free-standing Mathematics Qualifications
Ope.ls The first sheet is show elow. It is set up to show graphs with equatios of the form = m + c At preset the values of m ad c are oth zero. You ca chage these values usig the scroll ars. Leave the
More informationChapter 3 Classification of FFT Processor Algorithms
Chapter Classificatio of FFT Processor Algorithms The computatioal complexity of the Discrete Fourier trasform (DFT) is very high. It requires () 2 complex multiplicatios ad () complex additios [5]. As
More informationLecture 7 7 Refraction and Snell s Law Reading Assignment: Read Kipnis Chapter 4 Refraction of Light, Section III, IV
Lecture 7 7 Refractio ad Sell s Law Readig Assigmet: Read Kipis Chapter 4 Refractio of Light, Sectio III, IV 7. History I Eglish-speakig coutries, the law of refractio is kow as Sell s Law, after the Dutch
More informationImage Segmentation EEE 508
Image Segmetatio Objective: to determie (etract) object boudaries. It is a process of partitioig a image ito distict regios by groupig together eighborig piels based o some predefied similarity criterio.
More informationAdaptive Resource Allocation for Electric Environmental Pollution through the Control Network
Available olie at www.sciecedirect.com Eergy Procedia 6 (202) 60 64 202 Iteratioal Coferece o Future Eergy, Eviromet, ad Materials Adaptive Resource Allocatio for Electric Evirometal Pollutio through the
More informationBig-O Analysis. Asymptotics
Big-O Aalysis 1 Defiitio: Suppose that f() ad g() are oegative fuctios of. The we say that f() is O(g()) provided that there are costats C > 0 ad N > 0 such that for all > N, f() Cg(). Big-O expresses
More information27 Refraction, Dispersion, Internal Reflection
Chapter 7 Refractio, Dispersio, Iteral Reflectio 7 Refractio, Dispersio, Iteral Reflectio Whe we talked about thi film iterferece, we said that whe light ecouters a smooth iterface betwee two trasparet
More informationIMP: Superposer Integrated Morphometrics Package Superposition Tool
IMP: Superposer Itegrated Morphometrics Package Superpositio Tool Programmig by: David Lieber ( 03) Caisius College 200 Mai St. Buffalo, NY 4208 Cocept by: H. David Sheets, Dept. of Physics, Caisius College
More informationParabolic Path to a Best Best-Fit Line:
Studet Activity : Fidig the Least Squares Regressio Lie By Explorig the Relatioship betwee Slope ad Residuals Objective: How does oe determie a best best-fit lie for a set of data? Eyeballig it may be
More informationPython Programming: An Introduction to Computer Science
Pytho Programmig: A Itroductio to Computer Sciece Chapter 6 Defiig Fuctios Pytho Programmig, 2/e 1 Objectives To uderstad why programmers divide programs up ito sets of cooperatig fuctios. To be able to
More informationDescriptive Statistics Summary Lists
Chapter 209 Descriptive Statistics Summary Lists Itroductio This procedure is used to summarize cotiuous data. Large volumes of such data may be easily summarized i statistical lists of meas, couts, stadard
More informationCounting Regions in the Plane and More 1
Coutig Regios i the Plae ad More 1 by Zvezdelia Stakova Berkeley Math Circle Itermediate I Group September 016 1. Overarchig Problem Problem 1 Regios i a Circle. The vertices of a polygos are arraged o
More informationAN OPTIMIZATION NETWORK FOR MATRIX INVERSION
397 AN OPTIMIZATION NETWORK FOR MATRIX INVERSION Ju-Seog Jag, S~ Youg Lee, ad Sag-Yug Shi Korea Advaced Istitute of Sciece ad Techology, P.O. Box 150, Cheogryag, Seoul, Korea ABSTRACT Iverse matrix calculatio
More informationLecture 28: Data Link Layer
Automatic Repeat Request (ARQ) 2. Go ack N ARQ Although the Stop ad Wait ARQ is very simple, you ca easily show that it has very the low efficiecy. The low efficiecy comes from the fact that the trasmittig
More informationA Note on Least-norm Solution of Global WireWarping
A Note o Least-orm Solutio of Global WireWarpig Charlie C. L. Wag Departmet of Mechaical ad Automatio Egieerig The Chiese Uiversity of Hog Kog Shati, N.T., Hog Kog E-mail: cwag@mae.cuhk.edu.hk Abstract
More informationA New Morphological 3D Shape Decomposition: Grayscale Interframe Interpolation Method
A ew Morphological 3D Shape Decompositio: Grayscale Iterframe Iterpolatio Method D.. Vizireau Politehica Uiversity Bucharest, Romaia ae@comm.pub.ro R. M. Udrea Politehica Uiversity Bucharest, Romaia mihea@comm.pub.ro
More informationFundamentals of Media Processing. Shin'ichi Satoh Kazuya Kodama Hiroshi Mo Duy-Dinh Le
Fudametals of Media Processig Shi'ichi Satoh Kazuya Kodama Hiroshi Mo Duy-Dih Le Today's topics Noparametric Methods Parze Widow k-nearest Neighbor Estimatio Clusterig Techiques k-meas Agglomerative Hierarchical
More informationA SOFTWARE MODEL FOR THE MULTILAYER PERCEPTRON
A SOFTWARE MODEL FOR THE MULTILAYER PERCEPTRON Roberto Lopez ad Eugeio Oñate Iteratioal Ceter for Numerical Methods i Egieerig (CIMNE) Edificio C1, Gra Capitá s/, 08034 Barceloa, Spai ABSTRACT I this work
More informationFAST BIT-REVERSALS ON UNIPROCESSORS AND SHARED-MEMORY MULTIPROCESSORS
SIAM J. SCI. COMPUT. Vol. 22, No. 6, pp. 2113 2134 c 21 Society for Idustrial ad Applied Mathematics FAST BIT-REVERSALS ON UNIPROCESSORS AND SHARED-MEMORY MULTIPROCESSORS ZHAO ZHANG AND XIAODONG ZHANG
More informationBAYESIAN WITH FULL CONDITIONAL POSTERIOR DISTRIBUTION APPROACH FOR SOLUTION OF COMPLEX MODELS. Pudji Ismartini
Proceedig of Iteratioal Coferece O Research, Implemetatio Ad Educatio Of Mathematics Ad Scieces 014, Yogyakarta State Uiversity, 18-0 May 014 BAYESIAN WIH FULL CONDIIONAL POSERIOR DISRIBUION APPROACH FOR
More informationXIV. Congress of the International Society for Photogrammetry Hamburg 1980
XIV. Cogress of the Iteratioal Society for Photogrammetry Hamburg 980 Commissio V Preseted Paper ALTAN, M. O. Techical Uiversity of Istabul Chair of Photograrretry ad Adjustmet A COMPARISON BETWEEN -PARAMETER
More information9.1. Sequences and Series. Sequences. What you should learn. Why you should learn it. Definition of Sequence
_9.qxd // : AM Page Chapter 9 Sequeces, Series, ad Probability 9. Sequeces ad Series What you should lear Use sequece otatio to write the terms of sequeces. Use factorial otatio. Use summatio otatio to
More informationNormals. In OpenGL the normal vector is part of the state Set by glnormal*()
Ray Tracig 1 Normals OpeG the ormal vector is part of the state Set by glnormal*() -glnormal3f(x, y, z); -glnormal3fv(p); Usually we wat to set the ormal to have uit legth so cosie calculatios are correct
More informationComputers and Scientific Thinking
Computers ad Scietific Thikig David Reed, Creighto Uiversity Chapter 15 JavaScript Strigs 1 Strigs as Objects so far, your iteractive Web pages have maipulated strigs i simple ways use text box to iput
More informationIntro to Scientific Computing: Solutions
Itro to Scietific Computig: Solutios Dr. David M. Goulet. How may steps does it take to separate 3 objects ito groups of 4? We start with 5 objects ad apply 3 steps of the algorithm to reduce the pile
More informationLecture 5. Counting Sort / Radix Sort
Lecture 5. Coutig Sort / Radix Sort T. H. Corme, C. E. Leiserso ad R. L. Rivest Itroductio to Algorithms, 3rd Editio, MIT Press, 2009 Sugkyukwa Uiversity Hyuseug Choo choo@skku.edu Copyright 2000-2018
More informationSD vs. SD + One of the most important uses of sample statistics is to estimate the corresponding population parameters.
SD vs. SD + Oe of the most importat uses of sample statistics is to estimate the correspodig populatio parameters. The mea of a represetative sample is a good estimate of the mea of the populatio that
More informationOptimal Mapped Mesh on the Circle
Koferece ANSYS 009 Optimal Mapped Mesh o the Circle doc. Ig. Jaroslav Štigler, Ph.D. Bro Uiversity of Techology, aculty of Mechaical gieerig, ergy Istitut, Abstract: This paper brigs out some ideas ad
More informationOur Learning Problem, Again
Noparametric Desity Estimatio Matthew Stoe CS 520, Sprig 2000 Lecture 6 Our Learig Problem, Agai Use traiig data to estimate ukow probabilities ad probability desity fuctios So far, we have depeded o describig
More informationArithmetic Sequences
. Arithmetic Sequeces COMMON CORE Learig Stadards HSF-IF.A. HSF-BF.A.1a HSF-BF.A. HSF-LE.A. Essetial Questio How ca you use a arithmetic sequece to describe a patter? A arithmetic sequece is a ordered
More informationSorting in Linear Time. Data Structures and Algorithms Andrei Bulatov
Sortig i Liear Time Data Structures ad Algorithms Adrei Bulatov Algorithms Sortig i Liear Time 7-2 Compariso Sorts The oly test that all the algorithms we have cosidered so far is compariso The oly iformatio
More informationGE FUNDAMENTALS OF COMPUTING AND PROGRAMMING UNIT III
GE2112 - FUNDAMENTALS OF COMPUTING AND PROGRAMMING UNIT III PROBLEM SOLVING AND OFFICE APPLICATION SOFTWARE Plaig the Computer Program Purpose Algorithm Flow Charts Pseudocode -Applicatio Software Packages-
More informationLU Decomposition Method
SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS LU Decompositio Method Jamie Traha, Autar Kaw, Kevi Marti Uiversity of South Florida Uited States of America kaw@eg.usf.edu http://umericalmethods.eg.usf.edu Itroductio
More informationCMSC Computer Architecture Lecture 12: Virtual Memory. Prof. Yanjing Li University of Chicago
CMSC 22200 Computer Architecture Lecture 12: Virtual Memory Prof. Yajig Li Uiversity of Chicago A System with Physical Memory Oly Examples: most Cray machies early PCs Memory early all embedded systems
More informationFilter design. 1 Design considerations: a framework. 2 Finite impulse response (FIR) filter design
Filter desig Desig cosideratios: a framework C ı p ı p H(f) Aalysis of fiite wordlegth effects: I practice oe should check that the quatisatio used i the implemetatio does ot degrade the performace of
More informationCSC 220: Computer Organization Unit 11 Basic Computer Organization and Design
College of Computer ad Iformatio Scieces Departmet of Computer Sciece CSC 220: Computer Orgaizatio Uit 11 Basic Computer Orgaizatio ad Desig 1 For the rest of the semester, we ll focus o computer architecture:
More informationCOMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 4. The Processor. Part A Datapath Design
COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Iterface 5 th Editio Chapter The Processor Part A path Desig Itroductio CPU performace factors Istructio cout Determied by ISA ad compiler. CPI ad
More informationENGR 132. Fall Exam 1
ENGR 3 Fall 03 Exam INSTRUCTIONS: Duratio: 60 miutes Keep your eyes o your ow work. Keep your work covered at all times.. Each studet is resposible for followig directios. Read carefully.. MATLAB ad Excel
More informationDynamic Programming and Curve Fitting Based Road Boundary Detection
Dyamic Programmig ad Curve Fittig Based Road Boudary Detectio SHYAM PRASAD ADHIKARI, HYONGSUK KIM, Divisio of Electroics ad Iformatio Egieerig Chobuk Natioal Uiversity 664-4 Ga Deokji-Dog Jeoju-City Jeobuk
More informationBASED ON ITERATIVE ERROR-CORRECTION
A COHPARISO OF CRYPTAALYTIC PRICIPLES BASED O ITERATIVE ERROR-CORRECTIO Miodrag J. MihaljeviC ad Jova Dj. GoliC Istitute of Applied Mathematics ad Electroics. Belgrade School of Electrical Egieerig. Uiversity
More informationEVALUATION OF TRIGONOMETRIC FUNCTIONS
EVALUATION OF TRIGONOMETRIC FUNCTIONS Whe first exposed to trigoometric fuctios i high school studets are expected to memorize the values of the trigoometric fuctios of sie cosie taget for the special
More informationCS : Programming for Non-Majors, Summer 2007 Programming Project #3: Two Little Calculations Due by 12:00pm (noon) Wednesday June
CS 1313 010: Programmig for No-Majors, Summer 2007 Programmig Project #3: Two Little Calculatios Due by 12:00pm (oo) Wedesday Jue 27 2007 This third assigmet will give you experiece writig programs that
More informationForce Network Analysis using Complementary Energy
orce Network Aalysis usig Complemetary Eergy Adrew BORGART Assistat Professor Delft Uiversity of Techology Delft, The Netherlads A.Borgart@tudelft.l Yaick LIEM Studet Delft Uiversity of Techology Delft,
More informationChapter 3 MATHEMATICAL MODELING OF TOLERANCE ALLOCATION AND OVERVIEW OF EVOLUTIONARY ALGORITHMS
28 Chapter 3 MATHEMATICAL MODELING OF TOLERANCE ALLOCATION AND OVERVIEW OF EVOLUTIONARY ALGORITHMS Tolerace sythesis deals with the allocatio of tolerace values to various dimesios of idividual compoets
More informationPython Programming: An Introduction to Computer Science
Pytho Programmig: A Itroductio to Computer Sciece Chapter 1 Computers ad Programs 1 Objectives To uderstad the respective roles of hardware ad software i a computig system. To lear what computer scietists
More information1 Graph Sparsfication
CME 305: Discrete Mathematics ad Algorithms 1 Graph Sparsficatio I this sectio we discuss the approximatio of a graph G(V, E) by a sparse graph H(V, F ) o the same vertex set. I particular, we cosider
More informationA General Framework for Accurate Statistical Timing Analysis Considering Correlations
A Geeral Framework for Accurate Statistical Timig Aalysis Cosiderig Correlatios 7.4 Vishal Khadelwal Departmet of ECE Uiversity of Marylad-College Park vishalk@glue.umd.edu Akur Srivastava Departmet of
More informationExact Minimum Lower Bound Algorithm for Traveling Salesman Problem
Exact Miimum Lower Boud Algorithm for Travelig Salesma Problem Mohamed Eleiche GeoTiba Systems mohamed.eleiche@gmail.com Abstract The miimum-travel-cost algorithm is a dyamic programmig algorithm to compute
More informationCOMP 558 lecture 6 Sept. 27, 2010
Radiometry We have discussed how light travels i straight lies through space. We would like to be able to talk about how bright differet light rays are. Imagie a thi cylidrical tube ad cosider the amout
More informationRelay Placement Based on Divide-and-Conquer
Relay Placemet Based o Divide-ad-Coquer Ravabakhsh Akhlaghiia, Azadeh Kaviafar, ad Mohamad Javad Rostami, Member, IACSIT Abstract I this paper, we defie a relay placemet problem to cover a large umber
More information1. SWITCHING FUNDAMENTALS
. SWITCING FUNDMENTLS Switchig is the provisio of a o-demad coectio betwee two ed poits. Two distict switchig techiques are employed i commuicatio etwors-- circuit switchig ad pacet switchig. Circuit switchig
More informationAppendix D. Controller Implementation
COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Iterface 5 th Editio Appedix D Cotroller Implemetatio Cotroller Implemetatios Combiatioal logic (sigle-cycle); Fiite state machie (multi-cycle, pipelied);
More informationRunning Time. Analysis of Algorithms. Experimental Studies. Limitations of Experiments
Ruig Time Aalysis of Algorithms Iput Algorithm Output A algorithm is a step-by-step procedure for solvig a problem i a fiite amout of time. Most algorithms trasform iput objects ito output objects. The
More informationLecture Notes 6 Introduction to algorithm analysis CSS 501 Data Structures and Object-Oriented Programming
Lecture Notes 6 Itroductio to algorithm aalysis CSS 501 Data Structures ad Object-Orieted Programmig Readig for this lecture: Carrao, Chapter 10 To be covered i this lecture: Itroductio to algorithm aalysis
More informationRunning Time ( 3.1) Analysis of Algorithms. Experimental Studies. Limitations of Experiments
Ruig Time ( 3.1) Aalysis of Algorithms Iput Algorithm Output A algorithm is a step- by- step procedure for solvig a problem i a fiite amout of time. Most algorithms trasform iput objects ito output objects.
More informationAnalysis of Algorithms
Aalysis of Algorithms Iput Algorithm Output A algorithm is a step-by-step procedure for solvig a problem i a fiite amout of time. Ruig Time Most algorithms trasform iput objects ito output objects. The
More informationComputer Systems - HS
What have we leared so far? Computer Systems High Level ENGG1203 2d Semester, 2017-18 Applicatios Sigals Systems & Cotrol Systems Computer & Embedded Systems Digital Logic Combiatioal Logic Sequetial Logic
More informationCh 9.3 Geometric Sequences and Series Lessons
Ch 9.3 Geometric Sequeces ad Series Lessos SKILLS OBJECTIVES Recogize a geometric sequece. Fid the geeral, th term of a geometric sequece. Evaluate a fiite geometric series. Evaluate a ifiite geometric
More informationCoherent effects of flow- and pressure hull of a generic submarine on target scattering in an active sonar performance model
Coheret effects of flow- ad pressure hull of a geeric submarie o target scatterig i a active soar performace model P. Schippers TNO-D&V-Uderwater Techology, Oude Waalsdorperweg 63, Post Box 96864, 2509
More informationHow Reliable are the Ground Motion Prediction Equations?
20th Iteratioal Coferece o Structural Mechaics i Reactor Techology (SMiRT 20) Espoo, Filad, August 9-4, 2009 SMiRT 20-Divisio IV, Paper 662 How Reliable are the Groud Motio Predictio Equatios? Iztok Peruš
More informationPseudocode ( 1.1) Analysis of Algorithms. Primitive Operations. Pseudocode Details. Running Time ( 1.1) Estimating performance
Aalysis of Algorithms Iput Algorithm Output A algorithm is a step-by-step procedure for solvig a problem i a fiite amout of time. Pseudocode ( 1.1) High-level descriptio of a algorithm More structured
More information2D Isogeometric Shape Optimization considering both control point positions and weights as design variables
1 th World Cogress o tructural ad Multidiscipliary Optimizatio May 19-24, 213, Orlado, Florida, UA 2D Isogeometric hape Optimizatio cosiderig both cotrol poit positios ad weights as desig variables Yeo-Ul
More informationMarkov Chain Model of HomePlug CSMA MAC for Determining Optimal Fixed Contention Window Size
Markov Chai Model of HomePlug CSMA MAC for Determiig Optimal Fixed Cotetio Widow Size Eva Krimiger * ad Haiph Latchma Dept. of Electrical ad Computer Egieerig, Uiversity of Florida, Gaiesville, FL, USA
More informationStone Images Retrieval Based on Color Histogram
Stoe Images Retrieval Based o Color Histogram Qiag Zhao, Jie Yag, Jigyi Yag, Hogxig Liu School of Iformatio Egieerig, Wuha Uiversity of Techology Wuha, Chia Abstract Stoe images color features are chose
More informationA Polynomial Interval Shortest-Route Algorithm for Acyclic Network
A Polyomial Iterval Shortest-Route Algorithm for Acyclic Network Hossai M Akter Key words: Iterval; iterval shortest-route problem; iterval algorithm; ucertaity Abstract A method ad algorithm is preseted
More informationSERIAL COMMUNICATION INTERFACE FOR ESA ESTRO
Bulleti E708 rev0 7/06/0 SERIAL COMMUNICATION INTERFACE FOR - SERIES FEATURES Supply voltage: 90 40vac Supply frequecy: 40 70 Hz Max. absorbtio: 40W Operatig temperature: 0 50 C Storage temperature: -0
More informationFuzzy Minimal Solution of Dual Fully Fuzzy Matrix Equations
Iteratioal Coferece o Applied Mathematics, Simulatio ad Modellig (AMSM 2016) Fuzzy Miimal Solutio of Dual Fully Fuzzy Matrix Equatios Dequa Shag1 ad Xiaobi Guo2,* 1 Sciece Courses eachig Departmet, Gasu
More informationEigenimages. Digital Image Processing: Bernd Girod, 2013 Stanford University -- Eigenimages 1
Eigeimages Uitary trasforms Karhue-Loève trasform ad eigeimages Sirovich ad Kirby method Eigefaces for geder recogitio Fisher liear discrimat aalysis Fisherimages ad varyig illumiatio Fisherfaces vs. eigefaces
More informationAnalysis of Server Resource Consumption of Meteorological Satellite Application System Based on Contour Curve
Advaces i Computer, Sigals ad Systems (2018) 2: 19-25 Clausius Scietific Press, Caada Aalysis of Server Resource Cosumptio of Meteorological Satellite Applicatio System Based o Cotour Curve Xiagag Zhao
More informationMathematical Stat I: solutions of homework 1
Mathematical Stat I: solutios of homework Name: Studet Id N:. Suppose we tur over cards simultaeously from two well shuffled decks of ordiary playig cards. We say we obtai a exact match o a particular
More informationRecursive Procedures. How can you model the relationship between consecutive terms of a sequence?
6. Recursive Procedures I Sectio 6.1, you used fuctio otatio to write a explicit formula to determie the value of ay term i a Sometimes it is easier to calculate oe term i a sequece usig the previous terms.
More informationA PREDICTION MODEL FOR USER S SHARE ANALYSIS IN DUAL- SIM ENVIRONMENT
GSJ: Computer Sciece ad Telecommuicatios 03 No.3(39) ISSN 5-3 A PRDICTION MODL FOR USR S SHAR ANALYSIS IN DUAL- SIM NVIRONMNT Thakur Sajay, Jai Parag Orietal Uiversity, Idore, Idia sajaymca00@yahoo.com
More informationThe isoperimetric problem on the hypercube
The isoperimetric problem o the hypercube Prepared by: Steve Butler November 2, 2005 1 The isoperimetric problem We will cosider the -dimesioal hypercube Q Recall that the hypercube Q is a graph whose
More informationAnalysis of Documents Clustering Using Sampled Agglomerative Technique
Aalysis of Documets Clusterig Usig Sampled Agglomerative Techique Omar H. Karam, Ahmed M. Hamad, ad Sheri M. Moussa Abstract I this paper a clusterig algorithm for documets is proposed that adapts a samplig-based
More informationBig-O Analysis. Asymptotics
Big-O Aalysis 1 Defiitio: Suppose that f() ad g() are oegative fuctios of. The we say that f() is O(g()) provided that there are costats C > 0 ad N > 0 such that for all > N, f() Cg(). Big-O expresses
More information