An inter-laboratory study to quantify the repeatability, reproducibility, and bias of sound power measurement methods

Samuel Underwood 1

Lily Wang 2

Durham School of Architectural Engineering and Construction University of Nebraska-Lincoln 1110 S. 67th Street Omaha NE 68182

ABSTRACT An inter-laboratory study across multiple facilities has been completed to quantify the repeatability, reproducibility, and bias of three di ff erent sound power measurement methods used in the heating, ventilation, and air-conditioning industry: free field method, di ff use field method, and intensity method. The sound power levels of a loudspeaker source across one-third octave bands have been measured in each participating laboratory by the test methods preferred in those facilities. Both a broadband signal with decreasing slope of – 5 dB per octave band and the same broadband signal with four discrete tones at 58, 120, 300, and 600 Hz have been measured in this round robin study. Comparisons of measured sound power levels have been made between methods, between laboratories, and between laboratories using the same method. Repeatability, reproducibility, laboratory bias, and test method bias are then quantified in accordance with ISO 5725. [Work supported by the Air-Conditioning, Heating, and Refrigeration Institute]

1. INTRODUCTION

Sound power is a useful quantity for assessing the acoustic output of a noise source. Since it is distance independent, practitioners may directly compare sound powers from di ff erent sources or predict a resultant sound pressure level at discrete positions when environmental factors are known. Multiple sound power measurement standards have been developed, but the uncertainties associated with each standard have not been compared. This paper presents results to date from an inter-laboratory study to quantify the bias, reproducibility, and repeatability of three sound power measurement methods used in the heating, ventilation, air-conditioning, and refrigeration (HVACR) industry: direct comparison in a free field, sound intensity, and direct pressure comparison in a di ff use field.

1 samuelunderwood@huskers.unl.edu

2 lilywang@unl.edu

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2. BACKGROUND

Sound power ( W ) and sound power level ( S WL ) describe the rate of sound energy emission from a source. Multiple standardized methods for measuring sound power exist, and they can typically be attributed to one of three fundamental categories:

– Direct comparison of sound pressure level (SPL) in a di ff use field to a reference source – Intensity scanned across an enclosing surface – Surface averaged sound pressure level in a free field

2.1. Direct Comparison in a Di ff use Field The sound power of an acoustic source can be determined via direct comparison to the known sound power level of a reference sound source (RSS) when both the RSS and the test source are tested in the same di ff use field. Using Equation 1, room-averaged sound pressure level measurements for the RSS and the test source in a qualified reverberation chamber can be used to calculate the sound power of the test source ( L w ):

L W = L Wr + ( L P − L Pr ) (1)

where L Wr is the known sound power level of the RSS, L P is the room-averaged sound pressure level of the test source, and L Pr is the room-averaged sound pressure level of the RSS.

In this study, the direct comparison in a di ff use field method was implemented according to the AHRI 220 measurement standard [1]. A minor update to this standard is likely to be published before the end of 2022.

2.2. Intensity Method The sound power of an acoustic source may also be determined from measurements of acoustic intensity as scanned across an enclosing measurement surface. Intensity probe measurements are then integrated across the surface area of the enclosing measurement surface as expressed in Equation 2:

W = Z

S ⃗ I · ˆ n ds (2)

where ⃗ I is the sound intensity vector, S is the surface area of the enclosing measurement surface, and ˆ n is the unit vector normal to the enclosing surface.

In this study, the intensity method was implemented according to the ISO 9614-2 measurement standard [2].

2.3. Sound Pressure Level in a Free Field If an acoustic source is placed upon a reflecting plane with a surrounding free field, the sound power level of the source can be determined from sound pressure level measurements averaged across an enclosing measurement surface. As expressed in Equation 3, the average sound pressure level measurements are corrected according to the surface area of the measurement surface to determine sound power level:

L W = ¯ L P + 10 log ( S

S 0 ) (3)

where ¯ L P is the sound pressure level averaged across the measurement surface, S is the surface area of the measurement surface, and S 0 is 1 m 2 .

In this study, the pressure in a free field method was implemented according to the ISO 3744 measurement standard [3].

2.4. Measurement Uncertainty While each of the sound power measurement methods are defined by standardized procedures, there may exist contrasting measurement uncertainties between the methods. Sources of inter- laboratory and inter-method variation could include di ff erences in measurement chambers, sampling positions, equipment types, equipment calibrations, and correction factors. As such, the presence of systematic uncertainty should be explored.

3. METHODOLOGY

3.1. Repeatability Repeatability is defined as the within-lab precision under so-called "repeatability conditions" during which independent test results are obtained with the same method on the same test item(s) in the same measurement chamber by the same operator using the same measurement instruments within a short interval of time [4]. As depicted in Equation 4 this may be statistically expressed as a repeatability variance or repeatability standard deviation ( s r ):

v t

n X

1 n − 1 +

s r =

k = 1 ( y k − ¯ y ) (4)

where n is the number of measurements performed, y k is the k th measured value, and ¯ y is the mean of the measured values.

3.2. Reproducibility Reproducibility is defined as the closeness of agreement of values obtained under so-called "reproducibility conditions" during which values are obtained on an identical test item from di ff erent labs with di ff erent operators and di ff erent measurement instruments using the same measurement procedure. The reproducibility variance ( s R 2 ) is then the sum of the repeatability variance ( s r 2 ) and the between-lab variance ( s L 2 ). The between-lab variance is given by Equation 5:

s 2 L = s 2 d − s 2 r ¯¯ n (5)

where ¯ ¯ n is the mean number of measurements performed across participating laboratories, and s 2 d is the variance given by Equation 6.

p X

s 2 d = 1 p − 1

i = 1 n ( ¯ y i − ¯ ¯ y ) 2 (6)

where n is the number of all measurements performed, ¯ y i is the mean of the measured values within a particular lab, and ¯ ¯ y is the grand mean of the measured values across all labs.

3.3. Bias Bias is defined as the di ff erence between results obtained from one measurement method compared to an agreed upon reference value, which is influenced by the total systematic error. For this study, the accepted reference values were obtained by averaging results across labs that implemented the intensity method (governed by ISO 9614-2), since it is believed that the intensity method minimizes

the influence of environmental factors. The estimated bias of a particular measurement method ( ˆ δ ) is calculated according to Equation 7:

ˆ δ = ¯¯ y − µ (7)

where ¯ ¯ y is the mean of all measurements performed across all labs using that specific method and µ is the accepted reference value.

Results from one laboratory may be compared to the accepted reference value to estimate a laboratory bias ( ˆ ∆ ) as defined in Equation 8:

ˆ ∆= ¯ y i − µ (8)

where ¯ y i is the i th laboratory and µ is the accepted reference value.

Lastly, each laboratory may also introduce unique systematic error components, such that the di ff erence between an individual lab’s total laboratory bias ( ˆ ∆ ) and the measurement method bias ( ˆ δ ) can be calculated to determine the specific component of bias associated with the test conditions in a particular laboratory. This is defined by ISO 5725 as the laboratory component of bias. [4]

3.4. Test Protocol An inter-laboratory study was developed to investigate the repeatability, reproducibility, and bias of the three aforementioned sound power test methods. A common test source, playback device containing two test signals, and audio cables to connect the playback device to the test source were packaged into a test kit. The kit was shipped—in a round-robin configuration—to participating laboratories in North America for testing. Each laboratory measured the sound power level of the common source using whichever methods were preferred in that facility. Results from a total of 22 unique testing rooms were collected across all methods; some facilities had the capability of performing multiple methods in the same testing room or at multiple qualified positions.

The test source, depicted in Figure 1, was a directional stage monitor loudspeaker capable of producing sound across the 50 Hz to 10 kHz 1 / 3 octave band frequency range. Since many noise sources encountered in the HVACR industry are directional in nature, a non-omnidirectional source was favored.

Figure 1: Common sound source tested in each of the participating labs, packaged in shipping case

To create the two test signals for this study, 188 narrowband SPL spectra measurements of HVAC equipment (provided by the AHRI oversight committee) were sampled. From this analysis, two main

test signals were selected to represent the varying SPL spectra encountered in the HVACR industry.

The first test signal was selected to be a broadband spectrum with a -5 dB / octave slope intersecting at a SPL of 50 dB at 100 Hz. The second signal was selected to include four discrete frequency tones at 58, 120, 300, and 600 Hz superimposed upon the same broadband spectrum as the first signal. The SPL of each tone was set to be 10 dB above the corresponding 1 / 3 octave-band noise level.

4. RESULTS

Mean sound power level measurements calculated within each lab have been averaged to generate means across labs using the AHRI 220 method ( p = 16), the ISO 9614-2 method ( p = 8), and the ISO 3744 method ( p = 4) for both the broadband test signal in Figure 2 and the broadband signal with tones in Figure 3.

Figure 2: Comparison of measured sound power levels from common test source emitting a broadband signal, averaged across labs that followed a particular measurement standard

5. CONCLUSIONS

An inter-laboratory study has been conducted to determine the repeatability, reproducibility, and bias of three sound power test methods. In a round-robin configuration, each participating laboratory measured the sound power of the same directional test source. Two signals were included with the source to be tested in each lab: one with a negatively sloped broadband spectrum, and the other with a negatively sloped broadband spectrum with discrete tones. Preliminary means across participating laboratories have been calculated and reported for each of the three measurement methods considered in the study. Complete results for repeatability, reproducibility, and bias values will be presented at the conference and published at a later time.

0000! 0008 00€9 000S 000r OSLE 00Sz 0002 0091 OSZL 0001 008 0€9 00S oor GLE 0sz 002 O91 GCL OOL 08 €9 os —— ISO 9614-2 —— ISO 3744 — AHRI 220 ie) fo) LO © Ke) iro) ite) (oe) ito) fo} wo oO o o © © » 105 100 (M 21-01 81 GP) IMS 1/3 Octave Bands (Hz)

Figure 3: Comparison of measured sound power levels from common test source emitting a broadband with tones signal, averaged across labs that followed a particular measurement standard

ACKNOWLEDGEMENTS

The authors would like to acknowledge the AHRI Standard 1150 subcommittee for their financial support of this project, as well as the participating laboratories for contributing their time and e ff ort to this study. The authors would also like to acknowledge Dr. Matthew Blevins and Dr. Siu-Kit Lau for their extensive contributions to earlier phases of this project.

REFERENCES

[1] AHRI. Reverberation room qualification and testing procedures for determining sound power of HVAC equipment. Standard 220, Air-Conditioning, Heating, and Refrigeration Institute, 2014. [2] ISO. Acoustics: Determination of sound power levels of noise sources using sound intensity – part 2: Measurement by scanning. Standard 9614-2, International Organization for Standardization, 1997. [3] ISO. Acoustics: Reverberation room qualification and testing procedures for determining sound power of HVAC equipment – engineering methods for an essentially free field over a reflecting plane. Standard 3744, International Organization for Standardization, 2010. [4] ISO. Accuracy (trueness and precision) of measurement methods and results. Standard 5725, International Organization for Standardization, 1994.

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