Uncertainty evaluation in field measurements of airborne sound insulation

Transcription

1 Uncertanty evaluaton n feld measurements of arborne sound nsulaton R. L. X. N. Mchalsk, D. Ferrera, M. Nabuco and P. Massaran Inmetro / CNPq, Av. N. S. das Graças, 50, Xerém, Duque de Caxas, RJ, Brazl ranny xaver@yahoo.com.br 4009

2 The Brazlan Commttee of Cvl Engneerng presented a set of standards concernng the evaluaton of the performance of several topcs for buldngs up to fve floors. The acoustc performance s one of them. The standards are n approval process and measurements n real buldngs wll be necessary. Dfferent professonals usng dfferent equpment wll emt certfcates establshng whch levels of nsulaton a certan flat provdes and ts uncertantes. The expanded measurement uncertanty s necessary to make dfferent measurement results comparable. The nternatonal Gude to the Expresson of Uncertanty n Measurement, the ISO/IEC Gude 98 (GUM), s a wdely accepted document to assess and evaluate the uncertanty of a measurement result, and was used n ths work. The standards concernng sound nsulaton measurements are ISO 140 seres and ISO Uncertanty estmates are avalable only for the classcal technque descrbed n ISO 140, based on repeatablty and reproducblty tests performed n laboratores. Feld measurements present some characterstcs that can contamnate the results. Independent measurements were carred out n a sngle floor buldng usng ISO specfcatons and the ISO/IEC Gude 98 was appled to obtan the uncertanty for measurement results of arborne sound nsulaton between rooms n stu. 1 Introducton In Brazl, there s not yet an offcal standard establshng acceptable values for sound nsulaton between rooms, but a set of standards concernng the evaluaton of the performance of buldngs up to fve floors s close to be approved [1]. Acoustc performance s one of the topcs dsclosed n the project of standards. The sound nsulaton parameters shall be measured accordng to ISO 140 [2] and the sngle-number quanttes for arborne sound nsulaton ratng shall be determned accordng to ISO 717 [3]. The project of standards establshes mnmum, ntermedate and satsfactory acceptable values for some parameters. Once the new standards are approved, new buldngs shall comply at least wth the mnmum requrements. To compare results from measurements n several buldngs undertaken by dfferent professonals wth the acceptable values, the uncertantes of those measurements must be expressed, n order to compare ther results. The uncertanty of a measurement result s defned n the nternatonal Gude to the Expresson of Uncertanty n Measurement, the GUM [4], as a parameter, assocated wth the result of a measurement that characterzes the dsperson of the values that could reasonably be attrbuted to the measurand. The gude standardzes how to determne and evaluate the uncertanty of a measurement result. In ths current work, ISO/IEC Gude 98 [4] was used to estmate the uncertanty of feld measurements of arborne sound nsulaton between rooms carred out wth a new method descrbed n ISO [5]. 2 Arborne sound nsulaton The arborne sound nsulaton between rooms measured n stu can be characterzed by three parameters, defned n the nternatonal standard ISO [6]. They are: apparent sound reducton ndex - R, normalzed level dfference - D n, and standardzed level dfference - D nt, gven n Eqs. (1) to (3). All of them depend on the sound level dfference between the source and the recevng rooms, D, and on room characterstcs. R' D 10log S = + A D n A = D 10log A0 T DnT = D+ 10log (3) T0 Where S s the area of the separatng element n m 2 ; A s the equvalent sound absorpton area of the recevng room (A = 0.16 V/T), accordng to ISO 354 [7], n m 2 /Sabn; V s the volume of the recevng room n m 3 ; T s the reverberaton tme of the recevng room n s; A 0 s the reference absorpton area (A 0 = 10 m 2 ); and T 0 s the reference reverberaton tme (T 0 = 0.5 s). The sound level dfference D can be obtaned by two methods of measurement: the classcal and the new methods (transfer functon methods). In the classcal method, D s obtaned by the drect measurement of the sound pressure levels n both rooms and s expressed by Eq. (4), where L S and L R are the space and tme average sound pressure levels n the source and recevng rooms, respectvely, when the source room s beng excted, obtaned by the energetc average of the levels measured n dfferent mcrophone postons. Ths method s descrbed n ISO [6] and uses a random exctaton sgnal wth contnuous spectrum, as a whte or pnk nose, to excte the source room. D = L L (4) S R In the new method, D s obtaned after processng the mpulse response of the room or ts transfer functon, as expressed by Eq. (5), where H S and H R are the energetc space average acoustc transfer functons n the source and recevng rooms, respectvely, when the source room s beng excted. Ths method s descrbed n ISO [5, 8] and uses a determnstc exctaton sgnal, as the maxmum length sequence or the sweep sne. D = H S H R (5) Because of the random exctaton sgnal, the classcal method requres tme and spatal averagng n order to reduce the standard devatons, and t s normally tme consumng. On the other hand, the sgnals used n the new (1) (2) 4010

3 methods are determnstc, so they can be accurately reproduced, mprovng the repeatablty of the measurements. The standardzed level dfference between rooms, D nt, s one of the parameters consdered n the Brazlan project of standards. For walls between two adjacent dwellngs, the mnmum acceptable values for the weghted standardzed level dfference, D nt,w, range from 40 to 44 db, the ntermedate acceptable values range from 45 to 49 db, and the satsfactory values are equal or above 50 db. An uncertanty of ± 2 db s now acceptable for feld measurements of D nt,w between rooms. In acoustcs n general, and partcularly n sound nsulaton measurements, there s not a completely establshed procedure used on a broad scale to evaluate ther uncertantes. Part 2 of ISO 140 [9] presents some uncertanty estmatons, only for the classcal technque, based on repeatablty and reproducblty tests performed n some laboratores, but not based on ISO/IEC Gude 98 [4]. One should remember that n laboratores the uncertantes can be controlled, whereas feld measurements present some characterstcs that can contamnate the results, as feld condtons and tme varance. For new technques, there are even not repeatablty and reproducblty tests to estmate the uncertanty of the results. ISO [5] states that the new methods can have smlar or better precson relatve to the classcal method and that ISO/IEC Gude 98 [4] shall be used to evaluate the uncertanty of the results. 3 GUM s uncertanty evaluaton The result of a measurement s an estmate of the measurand y calculated as a functon of the estmates (x 1,x 2,...,x N ) of the nput quanttes (X 1,,X N ). The GUM [4] descrbes steps to evaluate the measurement uncertanty. The frst step s to specfy the measurand y and ts relaton wth the nput quanttes X. The next step s to lst the estmates x of the nput quanttes and the possble sources of uncertanty, quantfyng ther assocated uncertanty components u(x ). Fnally, the total uncertanty of the measurement result, called the combned standard uncertanty, u c (y), can be calculated by the law of propagaton of uncertanty, combnng all the uncertanty components. Eq.(6) gves the combned standard uncertanty for uncorrelated nput quanttes, where c are the senstvty coeffcents and u(x ) are the standard uncertantes assocated wth x. The senstvty coeffcents are the partal dervatves of y wth respect to x, c = y x. ( ) N u ( y) = c u ( x ) (6) [ ] 2 2 c = 1 The nterval wthn whch the value of the measurand s beleved to le wth a hgh level of confdence s obtaned by the expanded uncertanty U of a measurement. It s the product of a coverage factor k and the combned standard uncertanty of the measurement: U = k uc ( y). The coverage factor k s chosen based on the desred level of confdence. The uncertanty of a measurement comprses many sources and many components and t can be qute complcated to defne all these sources and components. The GUM dvdes the uncertanty components n two classes, A and B, dependng on the method used to estmate ther numercal values. Type A estmaton of uncertanty s obtaned from statstcal analyss of results of a seres of expermental measurements, lke standard devatons. The best estmate x of an nput quantty X s gven by the arthmetc mean X of n statstcally ndependent observatons, n repeatablty condtons. The assocated standard uncertanty u(x ) s gven by the average expermental standard devaton, u x = s X n. ( ) ( ) Type B evaluatons are those for whch there s no expermental data from a set of measurements to statstcally evaluate ther standard uncertantes, but there are probablty dstrbutons based on experence or other nformaton, lke calbraton certfcates, manufacturer s data, or the result of a prevous uncertanty evaluaton. 4 Uncertanty estmaton for measured D nt The measurand D nt, expressed n Eq. (3), was chosen for the uncertanty evaluaton because t s the parameter consdered n the Brazlan project of standards. Table 1 relates the nput quanttes wth ther senstvty coeffcents and assocated standard uncertantes, and Fg. 1 llustrates the cause and effect dagram, relatng the parameter wth ts nput quanttes and uncertanty sources. nput quanttes senstvty coeffcents standard uncertantes H S ( f ) 1 u (H S ) ( f ) H R ( f ) -1 u (H R ) ( f ) T ( f ) 10 log ( e) T f u (T) ( f ) ( ) Table 1 Input quanttes and senstvty coeffcents for the measurements of D nt H S resoluton repeatablty setup resoluton resoluton repeatablty T H R repeatablty setup D nt Fg. 1 Cause and effect dagrams for D nt The ndvdual uncertanty components for the nput quanttes were estmated from expermental measurements performed n repeatablty condtons and quantfed n terms of the average expermental standard devaton of the measured values. The repeatablty condtons were 4011

4 characterzed by the same n-stu stuaton, the same operator, and the same equpment. The resoluton, also called the readablty, depends on the roundng of the result and was also consdered as a source of uncertanty. The uncertanty components of the transfer functons produced by the equpment setup depend on a seres of contrbutons from: mcrophones, sound source, preamplfers, cables, multplexer, calbrator. All measurements were carred out n stable envronmental condtons, therefore, effects of temperature, humdty and atmospherc pressure varatons were neglected n the uncertanty evaluaton. 4.1 Input quanttes: acoustc transfer functons H S and H R The uncertanty estmates for the nput quanttes H S and H R followed the same procedure descrbed n ths secton, where the subscrpts S and R do not appear. The acoustc transfer functon n a frequency band can be determned by Eq. (7): ( ) ( ) H f = H f + δ H + δ H (7) meas. setup resoluton Where H meas. ( f ) s the average acoustc transfer functon obtaned n the expermental measurements, δh setup s the contrbuton of the uncertanty of the transfer functon produced by the equpment setup and δh resoluton s the contrbuton of the uncertanty orgnated from the resoluton of the equpment used n the measurements. δh setup and δh resoluton have null value (δh setup = 0 and δh resoluton = 0), but ther assocated uncertantes u(δh setup ) and u(δh resoluton ) may not be null. The uncertanty related wth the measured transfer functon H meas. s evaluated from the average expermental standard devaton calculated for n measurements, Eq. (8). The mean value H( f ) calculated for n measurements s the estmated result. s ( H meas. u( H meas. = (8) n The uncertanty related wth the equpment setup s calculated assumng a rectangular dstrbuton n an nterval of ± 0.5 db, consderng known contrbutons of the used nstrumentaton, as the non-flatness of the mcrophone and the non-lnearty of the sound analyzer n the frequency range, Eq.(9): 0.5 u( δ H setup ) = (9) 3 The uncertanty related wth the roundng of the equpment used to measure the transfer functons s calculated usng the assumpton of a rectangular dstrbuton for the resoluton, whch s 0.1 db. Eq. (10) expresses ths uncertanty source: u( δ H resoluton ) = (10) 3 Combnng all the uncertanty components related to the nput quanttes H S ( f ) and H R ( f ), the uncertanty can be estmated, Eq. (11) ( ( )) = ( meas. ( )) + ( δ setup ) + ( δ resoluton ) (11) u H f u H f u H u H 4.2 Input quantty: reverberaton tme T The uncertanty related to the reverberaton tme consdered the repeatablty of the measurements, wth the average expermental standard devatons, and the roundng of the results, expressed n Eqs. (12) to (14). s ( Tmeas. u( Tmeas. = (12) n u( δ T resoluton ) = 3 (13) 2 2 ( ( )) = ( meas. ( )) + ( δ resoluton ) (14) u T f u T f u T 4.3 Combnng the components uncertantes The law of propagaton of the uncertantes, presented n Eq. (6) and rewrtten n Eq. (15), was appled to obtan the fnal combned standard uncertanty u c (D nt ), consderng all the nput quanttes uncorrelated D nt 2 D nt 2 DnT 2 c( nt) = S + R + HS HR T ( ) ( ) ( ) u D u H u H u T 5 Measurement data (15) Data used n the calculaton of the uncertanty were obtaned from ndependent measurements carred out between two adjacent rooms n a sngle floor buldng. The source room volume s 65.8 m 3 and the recevng room volume s 51.4 m 3. The area of separatng wall s 13.0 m 2. The rooms are llustrated n Fg. 2. The number and postons of mcrophones and source comply wth the requrements n part 4 of ISO 140 [6]. To obtan spatal averagng, fve mcrophone postons n both rooms and two source postons n the source room were used, as shown n Fg. 2, where M ponts are the mcrophone postons and F ponts are the source postons. The measurements were performed wth one mcrophone n each room, smultaneously and successvely moved, wth the followng combnatons of postons: M11-M12, M21- M22, M31-M32, M41-M42, and M51-M52, each for both source postons. The reverberaton tme of the recevng room was measured n accordance wth ISO 354 [7]. SOURCE ROOM Fg. 2 Adjacent rooms RECEIVING ROOM 4012

5 The exctaton sgnal was a sngle sweep wth long duraton generated by the software Monkey Forest, drven to the amplfer and then to the sound source. The source used to excte the room was a dodecahedron loudspeaker wth subwoofer. The envronmental condtons kept constant durng measurements and the effectve sgnal-to-nose rato was satsfactory n the consdered frequency range. Fg. 3 presents the mean values of the standardzed level dfference, obtaned for thrd-octave bands from 100 Hz to 3150 Hz. The weghted standardzed level dfference, D nt,w s 39 db, determned wth the procedure descrbed n ISO [3]. Fg. 4 shows the contrbutons from the uncertanty components to D nt uncertanty measurement results, at the thrd-octave band centre frequency of 1000 Hz. Feld condtons at the recevng and source room have a determnant nfluence on the fnal measurement uncertanty and the transfer functons n the source room H S present hgher standard devatons than the transfer functon n the recevng room H R. Hr Hs1 T 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 (db) Fg. 4 Uncertanty contrbutons (values of y x u x ) n D nt results at 1000 Hz ( ) ( ) Fg. 3 D nt 6 Uncertanty results From the values of the expermental measurements, the combned standard uncertanty could be estmated and ts expanded uncertanty was obtaned for a level of confdence of approxmately 95%, for whch was calculated a coverage factor k = 2. Table 2 presents the results and ther expanded uncertantes as functons of the frequency for D nt. The values of the expanded uncertanty are hgher at low frequences, as expected n sound nsulaton measurements. Freq (Hz) D nt (db) U (D nt ) (db) Table 2 D nt and ts uncertantes The measurement uncertanty budget and the uncertanty contrbutons are very useful and shall be carefully analysed because they allow to fnd mportant factors for the measurement results and to take necessary actons to mprove the measurement procedure. To calculate the uncertantes of the sngle-number quantty, D nt,w, as descrbed n ISO [3], repeatablty and reproducblty tests wth smulaton technques, lke Monte Carlo, can be appled [11]. 7 Consderatons Ths work presented an ntal evaluaton of the standard uncertanty of the results for a set of feld ndependent measurements of sound nsulaton. The uncertanty estmaton s not an easy procedure, snce t s dffcult to dentfy all sources of uncertanty related to the measurand and a methodology to evdence ts metrologcal confdence should also be appled. The values obtaned for the uncertanty of the measurement results are lower than the Brazlan acceptable values, whch s 2 db. However, t should be remembered that only few sources of uncertanty and no correlaton between the nput quanttes were consdered n ths evaluaton. If more uncertanty sources were consdered, the fnal combned standard uncertanty would be hgher than the obtaned values. Another mportant pont s that these are results for a specfc feld stuaton condton n one specfc buldng; therefore, more nvestgatons need to be performed n several dfferent condtons. Due to the determnstc behavour of the exctaton sgnal, the standard devatons of the measurements performed wth the new method are smaller than wth the classcal method, and the uncertanty wth the new method s also smaller. Attenton shall be gven n order to evaluate the uncertanty and more detaled studes are necessary to 4013

6 better establsh the estmate of uncertantes n acoustcs, especally wth new measurement methods. Acknowledgments The authors acknowledge the support provded by CNPq - Natonal Scentfc Research Councl - Brazl. References [1] ABNT 02: /1 "Buldngs up to fve floors Performance, Part 1: General Requrements", Brazlan Assocaton of Techncal Standards (2005), n Portuguese [2] ISO 140, "Acoustcs Measurement of sound nsulaton n buldngs and of buldng elements", all parts, Internatonal Organzaton for Standardzaton [3] ISO 717-1, "Acoustcs Ratng of sound nsulaton n buldngs and of buldng elements - Part 1: Arborne sound nsulaton", Internatonal Organzaton for Standardzaton (1996) [4] ISO/IEC Gude 98, "Gude to the Expresson of Uncertanty n Measurement (GUM), Internatonal Organzaton for Standardzaton (1995) [5] ISO 18233, "Acoustcs Applcaton of new measurement methods n buldng and room acoustcs", Internatonal Organzaton for Standardzaton (2006) [6] ISO 140-4, "Acoustcs Measurement of sound nsulaton n buldngs and of buldng elements - Part 4: Feld measurements of arborne sound nsulaton between rooms", Internatonal Organzaton for Standardzaton (1998) [7] ISO 354, "Acoustcs Measurement of sound absorpton n a reverberaton room", Internatonal Organzaton for Standardzaton (2003) [8] R. Venegas, M. Nabuco, P. Massaran, "Sound Insulaton Evaluaton Usng Transfer Functon Measurements", Journal of Buldng Acoustcs 13, No. 1, (2006) [9] ISO 140-2, "Acoustcs Measurement of sound nsulaton n buldngs and of buldng elements - Part 2: Determnaton, verfcaton and applcaton of precson data", Internatonal Organzaton for Standardzaton (1991) [10] Wolfgang. A. Schmd, "Interaccón de la resolucón y la repetbldad en la ncertdumbre combnada", Smposo de Metrología 2004, 25 al 27 de Octubre, Mexco (2004) [11] V. Wttstock,, "On the Uncertanty of Sngle-Number Quanttes for Ratng Arborne Sound Insulaton", Acta Acustca unted wth Acustca 93, (2007) 4014