Accuracy of prediction methods for the improvement of impact sound pressure levels using floor coverings
|
|
- Beryl Hodge
- 5 years ago
- Views:
Transcription
1 Accuracy of predictio methods for the improvemet of impact soud pressure levels usig floor coverigs Daiel GRIFFIN 1 1 Marshall Day Acoustics, Australia ABSTRACT The improvemet of impact soud pressure levels from floor coverigs, ΔL, ca be measured usig the method detailed i Aex H of ISO 114-1:16. Maufacturers of floor coverigs readily provide ΔL measuremet data to aid the desig of floor costructios to achieve acoustic performace criteria. I the case of heavyweight floor costructios, which typically iclude a cocrete slab, it is also possible to predict the improvemet of impact soud pressure levels by cosiderig the floor coverig as a mass-sprig system. This paper provides a brief outlie of some available predictio methods. The accuracy of these methods is evaluated by compariso with published measuremet data. Keywords: Floor coverigs, tappig machie, uderlay I-INCE Classificatio of Subjects Number(s): INTRODUCTION A reasoable objective for the accuracy of methods for predictig the improvemet i impact souds pressure levels (ISPLs) usig floor coverigs is to replicate the accuracy of laboratory measuremets. This kid of objective provides a boud o predictio accuracy, i the best case, of beig equivalet to the accuracy of laboratory measuremets. I this sese, idicators of laboratory measuremet accuracy such as reproducibility are relevat for assessig the accuracy of predictios. Guidace o measuremet accuracy is reviewed briefly here ad, oce established, it is used as a idicator of variatio betwee the measuremet ad predictio of improvemet of ISPLs usig floor coverigs. Two separate predictio models are employed depedig o whether the floor coverig is flexible such as cork or rubber floorig or whether it comprises plate ad elastic elemets such as a tiled floor with resiliet uderlay. For each model, variatios betwee measuremet ad predictio data are evaluated for a rage of differet floor coverigs.. PREDICTION TOLERANCES I Australia, the relevat stadard for measurig the improvemet i ISPLs is AS ISO 14-8:6 (1). Equatio (5) from this stadard provides the followig expressio for the improvemet of ISPL usig floor coverigs, L: L L L (1) Here L ad L are, respectively, the ormalized ISPLs of a heavyweight stadard floor without ad with a floor coverig. More geerally, procedures for measurig the improvemet i ISPLs usig floor coverigs are documeted i the ISO 114 series of stadards, with equatio H.1 of ISO 114-1:16 () beig equivalet to equatio 1 above. Regardig the precisio of measuremets, Clause 7 of AS ISO 14-8:6 provides the followig remarks: 1 dgriffi@marshallday.com.au
2 It is required that the measuremet procedure gives satisfactory repeatability. This shall be determied i accordace with the method show i ISO 14- ad shall be verified from time to time, particularly whe a chage is made i the procedure or istrumetatio. A comparable set of remarks are provided i Clause 8 of ISO 114-3:1 (3). The quoted stadard, ISO 14-:1991 (4) provides oe-third octave bad ucertaity data for L measuremets i terms of both repeatability ad reproducibility. These two coditios are described i Table 1 below. Coditio Repeatability Reproducibility Table 1 Ucertaity coditios ISO :14 defiitio Coditio of measuremet that icludes the same measuremet procedure, same operators, same measurig system, same locatio Coditio of measuremet that icludes differet locatios, operators, measurig systems The source of the ucertaity data is reportedly: [ ] a set of 1 tests coducted i 1983 ivolvig four laboratories i Scadiavia usig a loosely istalled flexible PVC floorig cover [ ] havig a weighted impact soud improvemet idex L w of about 14dB 14-:1991 was formally superseded i 14 by the stadard ISO 1999:14 (5). This more recet stadard provides typical oe-third octave bad stadard ucertaity data for the reproducibility coditio (referred to as Situatio A i that stadard). The source of the stadard ucertaity data is oted as follows. They are derived from iter-laboratory measuremets accordig to ISO ad ISO 575- ad represet average values derived from measuremets o differet types of test specimes [ ] Figure 1 below provides a compariso of these differet sets of ucertaity data. I the figure the values of reproducibility stadard deviatio from ISO :14 are expressed as a expaded ucertaity with a coverage factor of From the figure it is apparet that the reproducibility stadard deviatio data from ISO :14 is broadly comparable to the sets of ucertaity data from the earlier stadard, although variatios i particular oe-third octave bads ca be proouced. The Reproducibility data show i Table 1 are used through the remaider of this paper as a geeral idicator of the accuracy of methods for predictio L.
3 db 1 Repeatability values (Table A.1, ISO 14-:1991) Reproducibility values (Table A.1, ISO 14-:1991) Reproducibility stadard deviatio (Table 6, ISO :14) Figure 1 - Examples of precisio toleraces for L measuremets 3. FLEXIBLE FLOOR COVERINGS 3.1 Predictio method Ver (6) provides the followig expressio for estimatig the improvemet of ISPLs usig flexible floor coverigs: L F log () F ' F ad F are the Fourier coefficiets without ad with a floor coverig respectively. Assumig a very stiff ad massive floor, the value of F is commoly estimated as: m F gh fall (3) T Here m (kg) is the mass of the ISO tappig machie hammer, T (s) is the time betwee hammer impacts, g (m/s ) is acceleratio due to gravity ad h fall (m) is the fall height of the hammer. Ver provides the followig equatio for F assumig a flexible floor coverig without dampig istalled o a very stiff floor: 1 f t F ' f m f t dt si cos (4) T T υ (m/s) is the hammer velocity at the time of impact, ad f is the resoace frequecy give by: f 1 1 s m 1 A h m E h 1 (5) Here s is the dyamic stiffess, A h is the area of the hammer impactig the floor coverig, E is the dyamic Youg s modulus ad h (m) is the floor coverig thickess. The resoace frequecy represets the oset of improvemet i ISPLs usig the floor coverig. Below the resoace frequecy, L is geerally expected to be.
4 Improvemet of ISPLs usig floor coverigs, db Whe dampig is cosidered as part of the model, the followig equatio for F applies where η is the loss factor: 1 f t t F ' e t t dt T si cos cos T (6) Where: ad. s m (7) m 4ms s m (8) m 3. Compariso of predictios ad measuremets The predictio model for flexible floor coverigs from equatios 6, 7 ad 8 has bee used to predict L values for a rage of floor coverigs for which laboratory measuremet data is published ad available. Figure ad Figure 3 below preset three examples of the compariso betwee measuremets ad predictios for floor coverigs comprisig oe or two layers of flexible material. 8 Measured (A) Measured (B) Predicted (A) Predicted (B) Figure - Compariso of measured ad predicted L values for: (A) mm rubber mattig, ad; (B) 6 mm rubber mattig.
5 Improvemet of ISPLs usig floor coverigs, db 8 Measured (A) Predicted (A) Figure 3 - Compariso of measured ad predicted L values for: 3. mm viyl plaks o 5 mm rubber uderlay The agreemet betwee measuremets ad predictios show i the figures above is geerally reasoable. However, such a limited set of comparisos does ot provide a robust overview of geeral accuracy. To quatify the accuracy over a wide rage of flexible floor coverigs, 5 comparisos have bee made betwee theory ad measuremets. Predictios were made for each floor coverig usig stated material properties where possible. Where material properties were ot explicitly provided, estimated values have bee used. I particular, the dyamic Youg s modulus, E, was ot commoly provided yet it has a sigificat effect o a flexible floor coverig s ability to reduce ISPLs. For example, E is a factor i equatio 5 for the resoace frequecy. Values of E were estimated with referece to ay relevat data o similar materials ad also to provide a predictio result that offered reasoable agreemet with the measuremet data. I this sese, the measuremet data has bee used to directly determie a effective dyamic Youg s modulus. Figure 4 below presets a summary of the comparisos. The figure shows the mea differece betwee predicted ad measured L values both for 1/3 octave bad cetre frequecies ad also the overall L w values. The error bars show for the mea differeces represet oe stadard deviatio. The figure also icludes the reproducibility values from ISO 14-:1991 ad ISO :14, as they were preseted i Figure 1 above. It is importat to recogise that these values, which effectively represet a 95% cofidece iterval, are ot strictly comparable with the error bars of the mea differeces (which show oe stadard deviatio). Rather, the reproducibility values are icluded to provide cotext to the rage of mea differeces betwee predictios ad measuremets. I this figure, ay cosideratio of the ISO values as cofidece itervals should be avoided.
6 Differece i Improvemet of ISPLS usig floor coverigs (Predicted - Measured), db 1 Mea 'Predicted - Measured' Improvemet i ISPLs usig floor coverigs Reproducibility stadard deviatio (Table 6, ISO :14) Reproducibility values (Table A.1, ISO 14-:1991) Figure 4 - Mea differece betwee predicted ad measured L values for 5 flexible floor coverigs It ca be see i the figure that the mea differece values ad stadard deviatios at lower frequecies are relatively small. This broadly correspods to the regio below the resoace frequecy, where L values are expected to be. Above approximately 4 Hz, the mea differece is a positive value ad the stadard deviatio values icrease oticeably. The mea differece i L w values is -1.3 db, with a stadard deviatio of.6 db. 4. COMPLEX FLOOR COVERINGS 4.1 Predictio method Cha et al (7) provides the followig expressio for estimatig the improvemet of ISPLs usig floor coverigs which iclude a rigid plate ad a elastic uderlay: F F ' 1 i 1 i i Z p M (9) ω is the agular frequecy, ω is the agular resoace frequecy, M (kg) is the mass of the rigid plate ad Z p is the poit impedace of that plate. Examples of complex floor coverigs iclude timber, tile ad screed fiished floor surfaces with a resiliet or flexible uderlay material beeath such as cork or rubber. 4. Compariso of predictios ad measuremets The predictio model for complex floor coverigs from equatio 9 has bee used to predict L values for a rage of floor coverigs where laboratory measuremet data is also available. Figure 5 below presets two examples of the compariso betwee measuremets ad predictios.
7 Improvemet of ISPLs usig floor coverigs, db 8 Measured (A) Measured (B) Predicted (A) Predicted (B) Figure 5 - Compariso of measured ad predicted L values for: (A) 7 mm ceramic tiles ad 5 mm screed o a 5 mm rubber uderlay, ad; (B) 55 mm screed o 4 mm rubber ad cork uderlay. The figure shows that agreemet betwee measuremets ad predictios is reasoable. It ca also be see from the figure that: The measured L values for system (A) are greater tha at frequecies below the estimated resoace frequecy at 5 Hz. This may be due to measuremet error, or perhaps due to the additioal mass beig added to the floor structure by the screed ad ceramic tiles. The measured L values for system (B) are egative i the oe-third octave frequecy rage from 8 Hz to 15 Hz. The likely coicides with the resoat frequecy which is estimated to be 13 Hz. I total, 59 differet complex floor coverigs have bee modeled for compariso with measuremets. Results of this compariso are preseted i Figure 6 below usig the same approach as that show i Figure 4 above for flexible floor coverigs. The Figure 4 commets about iterpretig reproducibility values also apply here.
8 Differece i Improvemet of ISPLS usig floor coverigs (Predicted - Measured), db 1 Mea 'Predicted - Measured' Improvemet i ISPLs usig floor coverigs Reproducibility stadard deviatio (Table 6, ISO :14) Reproducibility values (Table A.1, ISO 14-:1991) Figure 6 - Mea differece betwee predicted ad measured L values for 59 complex floor coverigs It ca be see i the figure that the mea differece values ad stadard deviatios at lower frequecies are relatively small ad are egative meaig that the predicted L values are o average lower tha measured i the frequecy rage that, typically, is below the resoace frequecy. The mea differece i L w values is -. db, with a stadard deviatio of.3 db. 5. CONCLUSION Two differet models for predictig the improvemet of ISPLs usig floor coverigs have bee reviewed. Comparisos have bee made with measured data to evaluate the accuracy of the predictios. For each model, the agreemet betwee measuremets ad predictios is reasoable, with a absolute mea differece of ot more tha. db ad a stadard deviatio of ot more tha.6db i each case. This extet of the observed variatios seems comparable to the predictio toleraces for laboratory measuremets of L, suggestig that the predictio models could be helpful i desigig heavyweight floor costructios for apartmets ad other oise sesitive spaces. ACKNOWLEDGEMENTS Keith Ballagh s cotiuig advice ad wisdom of soud isulatio topics is gratefully ackowledged.
9 REFERENCES 1. Stadards Australia, Australia Stadard 14-8 Acoustics - Measuremets of soud isulatio i buildigs ad buildig elemets, Part 8: Laboratory measuremets of the reductio of trasmitted impact oise by floor coverigs o a heavyweight stadard floor, Sydey, Australia, 6. Iteratioal Orgaisatio for Stadardizatio, Iteratioal Stadard ISO 114 Acoustics - Laboratory measuremet of soud isulatio of buildig elemets, Part 1: Applicatio rules for specific products (ISO 114-1:16), Geeva, Switzerlad, 16 3 Iteratioal Orgaisatio for Stadardizatio, Iteratioal Stadard ISO 114 Acoustics - Laboratory measuremet of soud isulatio of buildig elemets, Part 3: Measuremet of impact soud isulatio (ISO 114-3:1), Geeva, Switzerlad, 1 4 Iteratioal Orgaisatio for Stadardizatio, Iteratioal Stadard 14- Determiatio, verificatio ad applicatio of precisio data, Geeva, Switzerlad, Iteratioal Orgaisatio for Stadardizatio, Iteratioal Stadard ISO 1999 Acoustics - Determiatio ad applicatio of measuremet ucertaity i buildig acoustics Part 1: Soud isulatio, Geeva, Switzerlad, 14 6 Ver, I.L., Impact oise isolatio of composite floors, J Acoust Soc Am, 1971, 5(4): Cha, S-I., Chu, H-H., Isertio loss predictio of floatig floors used i ship cabis, Applied Acoustics, 7 8 Hopkis, C. Soud isulatio, Butterworth-Heiema, Oxford, 7. 9 Iteratioal Orgaisatio for Stadardizatio, Iteratioal Stadard ISO 114 Acoustics - Laboratory measuremet of soud isulatio of buildig elemets, Part 5: Requiremets for test facilities ad equipmet (ISO 114-5:1), Geeva, Switzerlad, 1
Measurement 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 information567. Research of Dynamics of a Vibration Isolation Platform
567. Research of Dyamics of a Vibratio Isolatio Platform A. Kilikevičius, M. Jurevičius 2, M. Berba 3 Vilius Gedimias Techical Uiversity, Departmet of Machie buildig, J. Basaavičiaus str. 28, LT-03224
More informationProvläsningsexemplar / Preview TECHNICAL REPORT INTERNATIONAL SPECIAL COMMITTEE ON RADIO INTERFERENCE
TECHNICAL REPORT CISPR 16-4-3 2004 AMENDMENT 1 2006-10 INTERNATIONAL SPECIAL COMMITTEE ON RADIO INTERFERENCE Amedmet 1 Specificatio for radio disturbace ad immuity measurig apparatus ad methods Part 4-3:
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 informationMCT242: Electronic Instrumentation Lecture 2: Instrumentation Definitions
Faculty of Egieerig MCT242: Electroic Istrumetatio Lecture 2: Istrumetatio Defiitios Overview Measuremet Error Accuracy Precisio ad Mea Resolutio Mea Variace ad Stadard deviatio Fiesse Sesitivity Rage
More informationTRACEABILITY SYSTEM OF ROCKWELL HARDNESS C SCALE IN JAPAN
HARDMEKO 004 Hardess Measuremets Theory ad Applicatio i Laboratories ad Idustries - November, 004, Washigto, D.C., USA TRACEABILITY SYSTEM OF ROCKWELL HARDNESS C SCALE IN JAPAN Koichiro HATTORI, Satoshi
More informationStatistical Analysis on Uncertainty for Autocorrelated Measurements and its Applications to Key Comparisons
Statistical Aalysis o Ucertaity for Autocorrelated Measuremets ad its Applicatios to Key Comparisos Nie Fa Zhag Natioal Istitute of Stadards ad Techology Gaithersburg, MD 0899, USA Outlies. Itroductio.
More informationANALYSIS OF EXPERIMENTAL ERRORS
ANALYSIS OF EXPERIMENTAL ERRORS All physical measuremets ecoutered i the verificatio of physics theories ad cocepts are subject to ucertaities that deped o the measurig istrumets used ad the coditios uder
More informationProbability, Expectation Value and Uncertainty
Chapter 1 Probability, Expectatio Value ad Ucertaity We have see that the physically observable properties of a quatum system are represeted by Hermitea operators (also referred to as observables ) such
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 informationIntroduction to Signals and Systems, Part V: Lecture Summary
EEL33: Discrete-Time Sigals ad Systems Itroductio to Sigals ad Systems, Part V: Lecture Summary Itroductio to Sigals ad Systems, Part V: Lecture Summary So far we have oly looked at examples of o-recursive
More informationAccuracy assessment methods and challenges
Accuracy assessmet methods ad challeges Giles M. Foody School of Geography Uiversity of Nottigham giles.foody@ottigham.ac.uk Backgroud Need for accuracy assessmet established. Cosiderable progress ow see
More information1 Inferential Methods for Correlation and Regression Analysis
1 Iferetial Methods for Correlatio ad Regressio Aalysis I the chapter o Correlatio ad Regressio Aalysis tools for describig bivariate cotiuous data were itroduced. The sample Pearso Correlatio Coefficiet
More informationStandard Test Method for Laboratory Measurement of Impact Sound Transmission Through Floor-Ceiling Assemblies Using the Tapping Machine 1
Desigatio: E 92 90 (Reapproved 1996) e1 Stadard Test Method for Laboratory Measuremet of Impact Soud Trasmissio Through Floor-Ceilig Assemblies Usig the Tappig Machie 1 This stadard is issued uder the
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 informationMONITORING THE STABILITY OF SLOPES BY GPS
MONITORING THE STABILITY OF SLOPES BY GPS Prof. S. Sakurai Costructio Egieerig Research Istitute Foudatio, Japa Prof. N. Shimizu Dept. of Civil Egieerig, Yamaguchi Uiversity, Japa ABSTRACT The stability
More informationReliability of steel flexural members according to EC in serviceability limit state
NSCC2009 Reliability of steel flexural members accordig to EC i serviceability limit state D. Hofi & A. Mårtesso Divisio of Structural Egieerig, Lud Uiversity, Lud, Swede ABSTRACT: To achieve a relatively
More informationThe standard deviation of the mean
Physics 6C Fall 20 The stadard deviatio of the mea These otes provide some clarificatio o the distictio betwee the stadard deviatio ad the stadard deviatio of the mea.. The sample mea ad variace Cosider
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 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 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 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 informationTopic 5 [434 marks] (i) Find the range of values of n for which. (ii) Write down the value of x dx in terms of n, when it does exist.
Topic 5 [44 marks] 1a (i) Fid the rage of values of for which eists 1 Write dow the value of i terms of 1, whe it does eist Fid the solutio to the differetial equatio 1b give that y = 1 whe = π (cos si
More informationa. For each block, draw a free body diagram. Identify the source of each force in each free body diagram.
Pre-Lab 4 Tesio & Newto s Third Law Refereces This lab cocers the properties of forces eerted by strigs or cables, called tesio forces, ad the use of Newto s third law to aalyze forces. Physics 2: Tipler
More informationPROFICIENCY TESTING ACTIVITIES OF FREQUENCY CALIBRATION LABORATORIES IN TAIWAN, 2009
PROFICIENCY TESTING ACTIVITIES OF FREQUENCY CALIBRATION LABORATORIES IN TAIWAN, 009 Huag-Tie Li, Po-Cheg Chag, Jia-Lu Wag, ad Chia-Shu Liao Natioal Stadard Time & Frequecy Lab., TL, Chughwa Telecom Co.,
More informationActivity 3: Length Measurements with the Four-Sided Meter Stick
Activity 3: Legth Measuremets with the Four-Sided Meter Stick OBJECTIVE: The purpose of this experimet is to study errors ad the propagatio of errors whe experimetal data derived usig a four-sided meter
More informationOverview. p 2. Chapter 9. Pooled Estimate of. q = 1 p. Notation for Two Proportions. Inferences about Two Proportions. Assumptions
Chapter 9 Slide Ifereces from Two Samples 9- Overview 9- Ifereces about Two Proportios 9- Ifereces about Two Meas: Idepedet Samples 9-4 Ifereces about Matched Pairs 9-5 Comparig Variatio i Two Samples
More information6.3 Testing Series With Positive Terms
6.3. TESTING SERIES WITH POSITIVE TERMS 307 6.3 Testig Series With Positive Terms 6.3. Review of what is kow up to ow I theory, testig a series a i for covergece amouts to fidig the i= sequece of partial
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 informationThermal characterization of an insulating material through a tri-layer transient method
Advaced Sprig School «Thermal Measuremets & Iverse techiques», Domaie de Fraço, Biarritz, March -6 05 T6 Thermal characterizatio of a isulatig material through a tri-layer trasiet method V. Félix, Y. Jaot,
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 information- E < p. ˆ p q ˆ E = q ˆ = 1 - p ˆ = sample proportion of x failures in a sample size of n. where. x n sample proportion. population proportion
1 Chapter 7 ad 8 Review for Exam Chapter 7 Estimates ad Sample Sizes 2 Defiitio Cofidece Iterval (or Iterval Estimate) a rage (or a iterval) of values used to estimate the true value of the populatio parameter
More informationNumber of fatalities X Sunday 4 Monday 6 Tuesday 2 Wednesday 0 Thursday 3 Friday 5 Saturday 8 Total 28. Day
LECTURE # 8 Mea Deviatio, Stadard Deviatio ad Variace & Coefficiet of variatio Mea Deviatio Stadard Deviatio ad Variace Coefficiet of variatio First, we will discuss it for the case of raw data, ad the
More informationTESTING OF THE FORCES IN CABLE OF SUSPENSION STRUCTURE AND BRIDGES
TSTING OF TH FORCS IN CABL OF SUSPNSION STRUCTUR AND BRIDGS Zhou, M. 1, Liu, Z. ad Liu, J. 1 College of the Muicipal Techology, Guagzhou Uiversity, Guagzhou. Guagzhou Muicipal ad Ladscape gieerig Quality
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 informationTrue Nature of Potential Energy of a Hydrogen Atom
True Nature of Potetial Eergy of a Hydroge Atom Koshu Suto Key words: Bohr Radius, Potetial Eergy, Rest Mass Eergy, Classical Electro Radius PACS codes: 365Sq, 365-w, 33+p Abstract I cosiderig the potetial
More informationGUIDELINES ON REPRESENTATIVE SAMPLING
DRUGS WORKING GROUP VALIDATION OF THE GUIDELINES ON REPRESENTATIVE SAMPLING DOCUMENT TYPE : REF. CODE: ISSUE NO: ISSUE DATE: VALIDATION REPORT DWG-SGL-001 002 08 DECEMBER 2012 Ref code: DWG-SGL-001 Issue
More information(7 One- and Two-Sample Estimation Problem )
34 Stat Lecture Notes (7 Oe- ad Two-Sample Estimatio Problem ) ( Book*: Chapter 8,pg65) Probability& Statistics for Egieers & Scietists By Walpole, Myers, Myers, Ye Estimatio 1 ) ( ˆ S P i i Poit estimate:
More informationThere is no straightforward approach for choosing the warmup period l.
B. Maddah INDE 504 Discrete-Evet Simulatio Output Aalysis () Statistical Aalysis for Steady-State Parameters I a otermiatig simulatio, the iterest is i estimatig the log ru steady state measures of performace.
More informationII. Descriptive Statistics D. Linear Correlation and Regression. 1. Linear Correlation
II. Descriptive Statistics D. Liear Correlatio ad Regressio I this sectio Liear Correlatio Cause ad Effect Liear Regressio 1. Liear Correlatio Quatifyig Liear Correlatio The Pearso product-momet correlatio
More informationREGRESSION (Physics 1210 Notes, Partial Modified Appendix A)
REGRESSION (Physics 0 Notes, Partial Modified Appedix A) HOW TO PERFORM A LINEAR REGRESSION Cosider the followig data poits ad their graph (Table I ad Figure ): X Y 0 3 5 3 7 4 9 5 Table : Example Data
More informationA NEW CLASS OF 2-STEP RATIONAL MULTISTEP METHODS
Jural Karya Asli Loreka Ahli Matematik Vol. No. (010) page 6-9. Jural Karya Asli Loreka Ahli Matematik A NEW CLASS OF -STEP RATIONAL MULTISTEP METHODS 1 Nazeeruddi Yaacob Teh Yua Yig Norma Alias 1 Departmet
More informationEstimation of a population proportion March 23,
1 Social Studies 201 Notes for March 23, 2005 Estimatio of a populatio proportio Sectio 8.5, p. 521. For the most part, we have dealt with meas ad stadard deviatios this semester. This sectio of the otes
More informationAnalysis of Experimental Data
Aalysis of Experimetal Data 6544597.0479 ± 0.000005 g Quatitative Ucertaity Accuracy vs. Precisio Whe we make a measuremet i the laboratory, we eed to kow how good it is. We wat our measuremets to be both
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 informationMA238 Assignment 4 Solutions (part a)
(i) Sigle sample tests. Questio. MA38 Assigmet 4 Solutios (part a) (a) (b) (c) H 0 : = 50 sq. ft H A : < 50 sq. ft H 0 : = 3 mpg H A : > 3 mpg H 0 : = 5 mm H A : 5mm Questio. (i) What are the ull ad alterative
More informationRead through these prior to coming to the test and follow them when you take your test.
Math 143 Sprig 2012 Test 2 Iformatio 1 Test 2 will be give i class o Thursday April 5. Material Covered The test is cummulative, but will emphasize the recet material (Chapters 6 8, 10 11, ad Sectios 12.1
More informationMath 257: Finite difference methods
Math 257: Fiite differece methods 1 Fiite Differeces Remember the defiitio of a derivative f f(x + ) f(x) (x) = lim 0 Also recall Taylor s formula: (1) f(x + ) = f(x) + f (x) + 2 f (x) + 3 f (3) (x) +...
More informationAssessment of extreme discharges of the Vltava River in Prague
Flood Recovery, Iovatio ad Respose I 05 Assessmet of extreme discharges of the Vltava River i Prague M. Holický, K. Jug & M. Sýkora Kloker Istitute, Czech Techical Uiversity i Prague, Czech Republic Abstract
More informationAnalysis of Experimental Measurements
Aalysis of Experimetal Measuremets Thik carefully about the process of makig a measuremet. A measuremet is a compariso betwee some ukow physical quatity ad a stadard of that physical quatity. As a example,
More informationDamped Vibration of a Non-prismatic Beam with a Rotational Spring
Vibratios i Physical Systems Vol.6 (0) Damped Vibratio of a No-prismatic Beam with a Rotatioal Sprig Wojciech SOCHACK stitute of Mechaics ad Fudametals of Machiery Desig Uiversity of Techology, Czestochowa,
More information717. Investigation of dynamic and precision characteristics of low frequency vibration measurement device
717. Ivestigatio of dyamic ad precisio characteristics of low frequecy vibratio measuremet device V. Volkovas, E. Uldiskas, M. Eidukevičiūtė Techological Systems Diagostics Istitute, Kauas Uiversity of
More informationSample Size Estimation in the Proportional Hazards Model for K-sample or Regression Settings Scott S. Emerson, M.D., Ph.D.
ample ie Estimatio i the Proportioal Haards Model for K-sample or Regressio ettigs cott. Emerso, M.D., Ph.D. ample ie Formula for a Normally Distributed tatistic uppose a statistic is kow to be ormally
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 informationDYNAMIC ANALYSIS OF BEAM-LIKE STRUCTURES SUBJECT TO MOVING LOADS
DYNAMIC ANALYSIS OF BEAM-LIKE STRUCTURES SUBJECT TO MOVING LOADS Ivaa Štimac 1, Ivica Kožar 1 M.Sc,Assistat, Ph.D. Professor 1, Faculty of Civil Egieerig, Uiverity of Rieka, Croatia INTRODUCTION The vehicle-iduced
More informationSenvion SE Franz-Lenz-Str. 1, Osnabrück, Germany
Iteratioal Wid Egieerig Coferece IWEC 014 WAVE INDUCED FATIGUE LOADS ON MONOPILES - NEW APPROACHES FOR LUMPING OF SCATTER TABLES AND SITE SPECIFIC INTERPOLATION OF FATIGUE LOADS M. SEIDEL Sevio SE Fraz-Lez-Str.
More informationAssessment and Modeling of Forests. FR 4218 Spring Assignment 1 Solutions
Assessmet ad Modelig of Forests FR 48 Sprig Assigmet Solutios. The first part of the questio asked that you calculate the average, stadard deviatio, coefficiet of variatio, ad 9% cofidece iterval of the
More informationMECHANICAL INTEGRITY DESIGN FOR FLARE SYSTEM ON FLOW INDUCED VIBRATION
MECHANICAL INTEGRITY DESIGN FOR FLARE SYSTEM ON FLOW INDUCED VIBRATION Hisao Izuchi, Pricipal Egieerig Cosultat, Egieerig Solutio Uit, ChAS Project Operatios Masato Nishiguchi, Egieerig Solutio Uit, ChAS
More informationStatistical Intervals for a Single Sample
3/5/06 Applied Statistics ad Probability for Egieers Sixth Editio Douglas C. Motgomery George C. Ruger Chapter 8 Statistical Itervals for a Sigle Sample 8 CHAPTER OUTLINE 8- Cofidece Iterval o the Mea
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 informationInfinite Sequences and Series
Chapter 6 Ifiite Sequeces ad Series 6.1 Ifiite Sequeces 6.1.1 Elemetary Cocepts Simply speakig, a sequece is a ordered list of umbers writte: {a 1, a 2, a 3,...a, a +1,...} where the elemets a i represet
More informationTests report No. 150/10 Determination of thermal transmittance according to SN EN
CENTRUM STAVEBNÍHO INŽENÝRSTVÍ, a. s. CENTRE OF BUILDING CONSTRUCTION ENGINEERING, Joit Stock Compay orkplace Zlí, K Cihel 304, 764 3 Zlí - Louky Door ad widow testig laboratory, heat ad acoustical egieerig
More informationCertification of solar glass
Certificatio of ar glass Stefa Bruold (sbruold@areergy.ch), Ueli Frei (ueli.frei@areergy.ch), SPF-HSR, Oberseestrasse 10, CH-8640 Rapperswil, Switzerlad, Fax +41 (055) 2224844 Abstract The performace of
More informationLecture 1 Probability and Statistics
Wikipedia: Lecture 1 Probability ad Statistics Bejami Disraeli, British statesma ad literary figure (1804 1881): There are three kids of lies: lies, damed lies, ad statistics. popularized i US by Mark
More informationConfidence intervals summary Conservative and approximate confidence intervals for a binomial p Examples. MATH1005 Statistics. Lecture 24. M.
MATH1005 Statistics Lecture 24 M. Stewart School of Mathematics ad Statistics Uiversity of Sydey Outlie Cofidece itervals summary Coservative ad approximate cofidece itervals for a biomial p The aïve iterval
More informationChapter 2 Descriptive Statistics
Chapter 2 Descriptive Statistics Statistics Most commoly, statistics refers to umerical data. Statistics may also refer to the process of collectig, orgaizig, presetig, aalyzig ad iterpretig umerical data
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 informationDISTRIBUTION LAW Okunev I.V.
1 DISTRIBUTION LAW Okuev I.V. Distributio law belogs to a umber of the most complicated theoretical laws of mathematics. But it is also a very importat practical law. Nothig ca help uderstad complicated
More informationThe improvement of the volume ratio measurement method in static expansion vacuum system
Available olie at www.sciecedirect.com Physics Procedia 32 (22 ) 492 497 8 th Iteratioal Vacuum Cogress The improvemet of the volume ratio measuremet method i static expasio vacuum system Yu Hogya*, Wag
More informationSTP 226 EXAMPLE EXAM #1
STP 226 EXAMPLE EXAM #1 Istructor: Hoor Statemet: I have either give or received iformatio regardig this exam, ad I will ot do so util all exams have bee graded ad retured. PRINTED NAME: Siged Date: DIRECTIONS:
More informationa b c d e f g h Supplementary Information
Supplemetary Iformatio a b c d e f g h Supplemetary Figure S STM images show that Dark patters are frequetly preset ad ted to accumulate. (a) mv, pa, m ; (b) mv, pa, m ; (c) mv, pa, m ; (d) mv, pa, m ;
More informationTests of Hypotheses Based on a Single Sample (Devore Chapter Eight)
Tests of Hypotheses Based o a Sigle Sample Devore Chapter Eight MATH-252-01: Probability ad Statistics II Sprig 2018 Cotets 1 Hypothesis Tests illustrated with z-tests 1 1.1 Overview of Hypothesis Testig..........
More informationANALYSIS OF DAMPING EFFECT ON BEAM VIBRATION
Molecular ad Quatum Acoustics vol. 7, (6) 79 ANALYSIS OF DAMPING EFFECT ON BEAM VIBRATION Jerzy FILIPIAK 1, Lech SOLARZ, Korad ZUBKO 1 Istitute of Electroic ad Cotrol Systems, Techical Uiversity of Czestochowa,
More information8. СОВЕТУВАЊЕ. Охрид, септември ANALYSIS OF NO LOAD APPARENT POWER AND FREQUENCY SPECTRUM OF MAGNETIZING CURRENT FOR DIFFERENT CORE TYPES
8. СОВЕТУВАЊЕ Охрид, 22 24 септември Leoardo Štrac Frajo Keleme Kočar Power Trasformers Ltd. ANALYSS OF NO LOAD APPARENT POWER AND FREQENCY SPECTRM OF MAGNETZNG CRRENT FOR DFFERENT CORE TYPES ABSTRACT
More informationThis is an introductory course in Analysis of Variance and Design of Experiments.
1 Notes for M 384E, Wedesday, Jauary 21, 2009 (Please ote: I will ot pass out hard-copy class otes i future classes. If there are writte class otes, they will be posted o the web by the ight before class
More informationµ and π p i.e. Point Estimation x And, more generally, the population proportion is approximately equal to a sample proportion
Poit Estimatio Poit estimatio is the rather simplistic (ad obvious) process of usig the kow value of a sample statistic as a approximatio to the ukow value of a populatio parameter. So we could for example
More informationExpected mean in an environmental noise measurement and its related uncertainty
Expected mea i a evirometal oise measuremet ad its related ucertaity M. Paviotti ad S. Kephalopoulos Europea Commissio, via e. fermi,, 00 Ispra, Italy marco.paviotti@jrc.it 85 I the cotext of the implemetatio
More informationA GERMAN CALIBRATION GUIDELINE FOR TORQUE WRENCH CALIBRATION DEVICES REVISED
XXI IEO World Cogress easuremet i Research ad Idustry August 30 September 4, 05, Prague, Czech Republic A GERAN CAIBRATION GUIDEINE FOR TORQUE WRENCH CAIBRATION DEVICES REVISED Dirk Röske Physikalisch-Techische
More informationSome Properties of the Exact and Score Methods for Binomial Proportion and Sample Size Calculation
Some Properties of the Exact ad Score Methods for Biomial Proportio ad Sample Size Calculatio K. KRISHNAMOORTHY AND JIE PENG Departmet of Mathematics, Uiversity of Louisiaa at Lafayette Lafayette, LA 70504-1010,
More informationChapter 2 Feedback Control Theory Continued
Chapter Feedback Cotrol Theor Cotiued. Itroductio I the previous chapter, the respose characteristic of simple first ad secod order trasfer fuctios were studied. It was show that first order trasfer fuctio,
More informationChapter 12 - Quality Cotrol Example: The process of llig 12 ouce cas of Dr. Pepper is beig moitored. The compay does ot wat to uderll the cas. Hece, a target llig rate of 12.1-12.5 ouces was established.
More informationPREDICTION OF REVERBERATION TIME IN RECTANGULAR ROOMS WITH NON UNIFORMLY DISTRIBUTED ABSORPTION USING A NEW FORMULA
PREDICTION OF REVERBERATION TIME IN RECTANGULAR ROOM WITH NON UNIFORMLY DITRIBUTED ABORPTION UING A NEW FORMULA PAC REFERENCE: 43.55.Br Neubauer, Reihard O. Ig.-Büro Neubauer VDI Theresiestr. 8 D-85049
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 informationComparing Two Populations. Topic 15 - Two Sample Inference I. Comparing Two Means. Comparing Two Pop Means. Background Reading
Topic 15 - Two Sample Iferece I STAT 511 Professor Bruce Craig Comparig Two Populatios Research ofte ivolves the compariso of two or more samples from differet populatios Graphical summaries provide visual
More informationSection 11.8: Power Series
Sectio 11.8: Power Series 1. Power Series I this sectio, we cosider geeralizig the cocept of a series. Recall that a series is a ifiite sum of umbers a. We ca talk about whether or ot it coverges ad i
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 informationNotes on the GSW function gsw_geostrophic_velocity (geo_strf,long,lat,p)
Notes o gsw_geostrophic_velocity Notes o the GSW fuctio gsw_geostrophic_velocity (geo_strf,log,lat,p) Notes made 7 th October 2, ad updated 8 th April 2. This fuctio gsw_geostrophic_velocity(geo_strf,log,lat,p)
More informationCENTRIFUGAL PUMP SPECIFIC SPEED PRIMER AND THE AFFINITY LAWS Jacques Chaurette p. eng., Fluide Design Inc. November 2004
CENTRIFUGAL PUMP SPECIFIC SPEE PRIMER AN THE AFFINITY LAWS Jacques Chaurette p. eg., Fluide esig Ic. November 004 www.fluidedesig.com There is a umber called the specific speed of a pump whose value tells
More informationConfidence interval for the two-parameter exponentiated Gumbel distribution based on record values
Iteratioal Joural of Applied Operatioal Research Vol. 4 No. 1 pp. 61-68 Witer 2014 Joural homepage: www.ijorlu.ir Cofidece iterval for the two-parameter expoetiated Gumbel distributio based o record values
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 informationMarkscheme May 2015 Calculus Higher level Paper 3
M5/5/MATHL/HP3/ENG/TZ0/SE/M Markscheme May 05 Calculus Higher level Paper 3 pages M5/5/MATHL/HP3/ENG/TZ0/SE/M This markscheme is the property of the Iteratioal Baccalaureate ad must ot be reproduced or
More informationDrive Technology \ Drive Automation \ System Integration \ Services. Data Sheet. Functional Safety Safety Characteristics for BE..
Drive Techology \ Drive Automatio \ System Itegratio \ Services Data Sheet Fuctioal Safety Safety Characteristics for BE.. Brake Editio 12/2010 17062810 / EN SEW-EURODRIVE Drivig the world Data Sheet Safety
More informationStatistical Inference About Means and Proportions With Two Populations
Departmet of Quatitative Methods & Iformatio Systems Itroductio to Busiess Statistics QM 220 Chapter 10 Statistical Iferece About Meas ad Proportios With Two Populatios Fall 2010 Dr. Mohammad Zaial 1 Chapter
More informationFrequentist Inference
Frequetist Iferece The topics of the ext three sectios are useful applicatios of the Cetral Limit Theorem. Without kowig aythig about the uderlyig distributio of a sequece of radom variables {X i }, for
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 information1 Lesson 6: Measure of Variation
1 Lesso 6: Measure of Variatio 1.1 The rage As we have see, there are several viable coteders for the best measure of the cetral tedecy of data. The mea, the mode ad the media each have certai advatages
More informationFirst, note that the LS residuals are orthogonal to the regressors. X Xb X y = 0 ( normal equations ; (k 1) ) So,
0 2. OLS Part II The OLS residuals are orthogoal to the regressors. If the model icludes a itercept, the orthogoality of the residuals ad regressors gives rise to three results, which have limited practical
More informationHypothesis Testing. Evaluation of Performance of Learned h. Issues. Trade-off Between Bias and Variance
Hypothesis Testig Empirically evaluatig accuracy of hypotheses: importat activity i ML. Three questios: Give observed accuracy over a sample set, how well does this estimate apply over additioal samples?
More informationChapter 6 Part 5. Confidence Intervals t distribution chi square distribution. October 23, 2008
Chapter 6 Part 5 Cofidece Itervals t distributio chi square distributio October 23, 2008 The will be o help sessio o Moday, October 27. Goal: To clearly uderstad the lik betwee probability ad cofidece
More informationDEPARTMENT OF ACTUARIAL STUDIES RESEARCH PAPER SERIES
DEPARTMENT OF ACTUARIAL STUDIES RESEARCH PAPER SERIES Icreasig ad Decreasig Auities ad Time Reversal by Jim Farmer Jim.Farmer@mq.edu.au Research Paper No. 2000/02 November 2000 Divisio of Ecoomic ad Fiacial
More information