The three parts of ISO 9614 describe methods for the determination of the sound power level of noise sources. According to these standards, measured sound power levels must be qualified by comparing several sound field indicators to given criteria. This procedure is investigated by analytical calculations with monopole and dipole sources. Their sound fields are superposed with extraneous free and diffuse sound fields. When the ISO 9614 method is applied to these cases, it turns out that the signed pressure intensity indicator is well suited to qualify the measured sound power level. In contrast to this, the unsigned pressure intensity indicator and the field non-uniformity indicator fail to describe the quality of the determined sound power level. This theoretical finding is verified by a large measurement program.

## I. INTRODUCTION

The sound power level (SWL) $ L W$ is the key quantity to describe the noise emissions of products, machines, and equipment. For example, the following regulations use the SWL to describe the noise emission of some or all of the products in their scope: the European Outdoor Noise Directive,^{1} the Australian approach to noise labelling,^{2,3} the European Machinery Directive,^{4} and the EU energy label for certain products in the scope of the European Ecodesign Directive.^{5,6}

Furthermore, the SWL of machines, products, and equipment is the input quantity for the prediction of sound pressure levels^{7,8} in workshops and other rooms, where these products are operated. This prediction supports the safe and ergonomic design of factories, workshops, etc. with regard to noise and allows for the evaluation of the effects of room acoustic treatments and other noise control measures before they are implemented.

Thus, determining the SWL is important for environmental protection, for occupational health and safety, for product safety, and to inform consumers about the performance of a product regarding its noise emission. Ten different international standards can be used to determine the SWL. They differ on the required measurement equipment and the acoustic environment and yield results with different grades of accuracy.

These standards (see ISO 3740^{9} for an overview) can be divided into two main groups: those based on measuring the sound pressure level—the ISO 3740^{9} series of standards—and those based on measuring the sound intensity—the ISO 9614 set of standards (Parts 1–3).^{10–12} The former rely on cheaper measurement equipment but encounter more restrictions regarding the acoustic environment. Here, the measurements must either be performed in special acoustic environments—hemi-anechoic chambers, reverberation rooms, or outdoors—or be corrected regarding reflections in the room, the so-called environmental correction, and the background noise.

Outside of acoustic test facilities but indoors, one often finds that no measurements with sufficient accuracy, e.g., engineering grade, can be performed or that the conditions do not allow for a measurement that is compliant with the standard at all, e.g., because the environmental correction exceeds the limit in the standard used. In contrast to this, the sound intensity method works well outside of acoustic test facilities, and its application is mainly limited by the level and stationarity of the background noise, if present.

Nevertheless, the methods based on sound pressure measurements are more frequently used. ISO 3744^{13} is referred to in the European Outdoor Noise Directive^{1} and in many machine-specific noise test codes and safety standards, so-called C-standards in the European standardization jargon.

There are several potential reasons why the sound intensity method is rarely used despite its advantages. The current version of the ISO 9614^{10–12} set of standards uses partly inconsistent terminology. The older parts, ISO 9614-1^{10} and ISO 9614-2,^{11} date to 1993 and 1996, respectively; have not been revised since; and, apparently, do not correspond to the state-of-the-art. Recent technological and scientific advances have yet to be included in these standards (see also Sec. II). These standards use three major field indicators to assess the quality of the measured SWL. Depending on their values, more measurement points or even a completely new measurement, e.g., on another measurement surface, might be necessary to achieve the desired grade of accuracy. Still, in certain sound field situations, one might have no result regarding the SWL in the end. This approach makes determining the SWL with the sound intensity method quite laborious and complicated.

This paper aims at proposing ways to simplify and improve the sound intensity method. We present results regarding the correlation between the currently used field indicators and the deviation of the measured SWL from the actual SWL. The results hint at the fact that there might be room for simplification of the sound intensity method by using fewer field indicators to assess the quality of the measured SWL.

Section II describes the current knowledge regarding the relation between measured SWLs and the indicator-based standardized criteria for the intensity measurement method. The paper continues with a theoretical investigation of the correlation of the currently used field indicators with the deviation of the measured SWL from the actual SWL in Sec. III. Section IV shows the results of experiments that aim to test whether or not the theoretical results can be confirmed by measurements, while Sec. V presents the conclusions based on Secs. III and IV.

## II. INVESTIGATED INDICATORS AND CRITERIA IN ISO 9614

The intensity method for the determination of sound power is an enveloping surface method. This means that the normal component of the sound intensity is measured on a hypothetical surface enveloping the source under test. Sound field indicators are local or surface-averaged quantities that are “intended to help the experimenter in evaluating and interpreting experimental data.”^{14} In the specific case of ISO 9614,^{10–12} they are used in combination with given criteria to assess the measurement conditions to achieve a desired grade of accuracy of the measured SWL. As an intermediate step, modifications of the measurement setup like increasing or decreasing the measurement distance, increasing the number of discrete measurement points, or increasing the scan line density may be necessary. In certain very unfavorable field situations, it is possible that no valid SWL can be obtained according to ISO 9614-1.^{10}

^{15,16}

^{16}

^{,}

^{16}

^{,}

^{10–12}require

^{10–12}require, furthermore, that

^{10}the minimum number of measurement positions is

^{10}For precision and engineering grade, the standard deviation of reproducibility depends on frequency, and so does the factor $C$. It is between 11 and 57. For survey grade, only the A-weighted SWL is considered. $C$ is 8 in this case. This criterion has been in discussion for some time (see, e.g., Jacobsen

^{14}and Hübner

^{17}). There are further indicators and criteria used in ISO 9614

^{10–12}that are not examined in this contribution.

## III. THEORETICAL INVESTIGATION ON THE USEFULNESS OF SELECTED INDICATORS

### A. Basic approach

To investigate the usefulness of the indicators introduced in clause II, field configurations with single monopoles and single dipoles are considered. The sound pressure field created by these sources is superposed by a plane wave and an additional diffuse field, both of varying amplitude. The resulting sound field around the sound sources is sampled at *N* field points on an enveloping hemisphere or sphere by a p-p probe with an assumed pressure**-**residual intensity index δ_{pI}_{0}. The field point distribution is chosen so that each point represents the same area. The SWL obtained from this simulated measurement is finally compared to the known SWL of the monopole or dipole as a function of the standardized indicators from clause II.

### B. Monopole

#### 1. Theoretical model

#### 2. Calculation results for very large numbers of measurement points

Due to symmetry, only the upper hemisphere of a surrounding sphere is discretized by a mesh of 2117 points, which acceptably represent equal areas (Fig. 1). The difference between the measured and the theoretical SWL of the monopole is then obtained by averaging the related intensity from Eq. (15). Surface averaging of the related pressure and of the modulus of the related intensity then enables a calculation of the indicators $ F p I n$ and $ F p I n$, whereas the minimum number of discrete measurement points is calculated from Eq. (12) with the indicator $ F S$ from Eq. (11).

The SWL difference, i.e., the difference between the measured SWL and the known SWL of the monopole, is a clear function of the pressure intensity criterion $ F p I n\u2212 \delta p I 0$ (Fig. 2). For very small values of $ F p I n\u2212 \delta p I 0$, the SWL difference approaches 0 dB, as expected. There are two branches obtained, one for $sgn \Delta \varphi =1$ and one for $sgn \Delta \varphi =\u22121$. The nature of the extraneous sound field does not influence the result at all. Therefore, all three curves are identical. It is furthermore noticeable that these results match excellently the theoretical result from Eq. (5), thereby validating the calculation model. Figure 2 indicates clearly that limiting $ F p I n\u2212 \delta p I 0$ to certain values is appropriate to limit the SWL difference.

When the SWL difference is plotted as a function of the difference between the unsigned and the signed pressure intensity indicators $ F p I n\u2212 F p I n$, different curves are obtained for different sound fields (Fig. 3). Whereas large values of the indicator correlate with large SWL deviations for the predominantly free external field ( $ b r/ a r=0.1$) and the mixed extraneous field ( $ b r/ a r=1$), the indicator totally fails for the predominantly diffuse field ( $ b r/ a r=10$). A limitation of the SWL difference by an application of an upper limit for $ F p I n\u2212 F p I n$, thus, requires knowledge of the nature of the sound field.

Similarly, the relation between the SWL difference and the minimum number of measurement points calculated according to Eq. (12) shows significant differences depending on the nature of the extraneous sound field (Fig. 4). The direct calculation result for the minimum number of measurement points is presented here on a logarithmic scale to handle the huge dynamic range. Of course, sound power determinations with less than one measurement point are not possible. For the predominantly diffuse extraneous field, relatively small numbers of points are sufficient, whereas for the dominant plane extraneous wave, much larger point numbers are calculated from Eq. (12). This result clearly demonstrates the physical meaning of the SWL difference, which is the difference between the measured SWL and the true SWL. This SWL difference is a systematic error or bias that cannot be reduced by using more measurement points on the enveloping surface. As for Fig. 3, it is, thus, questionable whether the application of the criterion (12) is appropriate to limit the SWL difference.

#### 3. Calculation results for a smaller number of measurement points

The result from the previous clause is that the SWL difference is a clear function of $ F p I n\u2212 \delta p I 0$, whereas the SWL difference depends on the nature of the extraneous sound field for $ F p I n\u2212 F p I n$ and $ N min$. However, these three criteria are not alternatively used but additionally in ISO 9614-1,^{10} i.e., the result has to be qualified according to all three criteria. To simulate this situation and to use a more reasonable number of measurement points, a spherical array of 12 points with equal point density is used for further calculation. It covers a full sphere. Discrete measurement points are located at the center points of the surfaces of a circumferential regular dodecahedron. Altogether, 1000 random representations with equal distributions are chosen, where $ \delta p I 0$ is between 10 and 25 dB and the relative amplitudes $ a r$ and $ b r$ are between 0 and 5. Additionally, the orientation of the spherical array is randomly chosen. The result is then treated like a measurement result according to ISO 9614-1.^{10} All calculated data points lie exactly on the curve defined by Eq. (5). These results are then classified according to criterion (8). The current thresholds of 10 and 7 dB are effectively limiting the SWL deviation to below ±0.5 or ±1.0 dB (Fig. 5). Calculation results that do not fulfill criterion (8) are disqualified and not shown in Fig. 5.

According to ISO 9614-1,^{10} results have to additionally comply with criterion (9). For the set of calculation results complying with criterion (8), this test is shown in Fig. 6. There is no correlation at all of the SWL difference with $ F p I n\u2212 F p I n$. Disqualifying all results that do not comply with criterion (9) is, therefore, totally unnecessary.

A similar result is obtained for criterion (12). In the considered case, 12 points are used. The calculation of the indicator $ F S$ in combination with the assumption of a survey method ( $C=8$) leads to a disqualification of a large amount of results although their SWL deviation is well within the desired limits (Fig. 7).

### C. Dipole

#### 1. Theoretical model

#### 2. Calculation results

For infinitely large numbers of measurement points, calculation results are qualitatively identical to the monopole case. For the sake of brevity, they are therefore not presented here.

Then the 12-point array described in Sec. III B 3 was used. Again, 1000 random calculations were performed with random lateral orientation of the array and equal distributions of $ \delta p I 0$ between 10 and 25 dB and $ a r$ and $ b r$ between 0 and 2. The upper limits of the relative sound pressure amplitudes are smaller than for the presented monopole results, because they are related to the sound pressure of the dipole in its maximum direction [Eq. (24)].

The calculation results for the power level difference $\Delta L W$ as a function of $ F p I n\u2212 \delta p I 0$ and $ F p I n\u2212 F p I n$ are identical to Figs. 5 and 6. Therefore, they are not shown again. A clear difference from the monopole case is observed for the power level difference $\Delta L W$ as a function of $ N min$ (Fig. 8). The indicator $ F S$ is much larger than for the monopole case since the spatial variation of the sound field is much larger. Therefore, a larger number of measurement points is required according to Eq. (12) for the dipole (Fig. 8) compared to the monopole (Fig. 7). Still, to limit the SWL deviation, an application of criterion (8) is absolutely sufficient, whereas criterion (12) unnecessarily disqualifies correct measurement results.

## IV. EXPERIMENTAL VERIFICATION

### A. Sources and surrounding environments

A major aim of the contribution was to perform measurements to verify the theoretical findings. Two main topics stand out from the theoretical calculations. The first is the utility of the $ F p I n \u2212 F p I n$ criterion, and the second is the minimum number of the required measurement points $ N min$. The difference between the pressure intensity indices is related to the presence of extraneous noise and/or strong reverberation, whereas the number of points is related to the field non-uniformity.^{10–12} The measurements were structured to cover a wide range of sources, environments, background noise characteristics, and other influential parameters, and apparently, it is assumed they can be used for supporting the ISO 9614^{10–12} revision proposals.

*i*th one-third octave band from 20 Hz to 20 kHz rounded to the nearest decade, and $ \phi i$ the related phase. The latter was randomly generated for each discrete frequency once. Then it was used for all TS measurements for repeatability reasons. To account for any changes in the sound emission of the TS, a correction was applied. It is given by

BSWA and TSWA are modifications of BS and TS, respectively. For the modification, an absorbing panel was added to each source at a defined position. For BSWA, the panel covered the open side of the box. The absorber had a thickness of 100 mm and a surface of 0.7 m^{2}. It was made of a polyester fiber mat, which is framed by a U-shaped aluminum profile.

Measurements were performed in five rooms, Physikalisch-Technische Bundesanstalt (PTB)'s hemi-anechoic room, PTB's 200 m^{3} reverberation room, an open space (a basement), a 50 m^{3} reverberant room, and the same room after adding absorption. For variation purposes, the hemi-anechoic room was used in two different states. In the first, the room was used as normal, while in the second, reflections were added. This was realized by adding ten reflecting panels of 0.7 m^{2} each. They were placed in front of the wedges on two orthogonal sides of the room, five on each side.

### B. Probe positioning

Following the guidelines of the ISO 9614^{10–12} series, measurements were performed either by scanning or at discrete points. The movement or positioning of the probes was performed both by automated means and manually. Three sound intensity probes were used, accommodating Brüel & Kjaer phase-matched microphone pairs.^{18} Three pairs of type 4181 and one of type 4197 were available for selection. For each measurement, two pairs of type 4181 and type 4197 were connected to the intensity probes.

#### 1. Automated measurements

The automated measurements were performed in PTB's hemi-anechoic room using PTB's scanning apparatus,^{19} covering a hemispherical measurement surface of 1.7 m radius. The scanning apparatus was placed inside PTB's hemi-anechoic room, which is qualified according to ISO 26101-1^{20} for frequencies between 50 Hz and 20 kHz for the measurement radii used. For the full scan of the hemisphere, the three probes covered once the left quarter sphere and afterward the right quarter sphere. For the measurements at discrete points, the arc movement was remotely stopped at predefined positions, occurring at 15°, 45°, 75°, 105°, 135°, and 165° (angle between the floor and the arc). This provided 36 measurement points.

A preliminary investigation was about the influence of the scanning speed. It must be noted that the speed of each probe is different due to its position on the scanning apparatus. Measurements were performed for three different measurement durations, namely, *T* = 600 s, *T* = 900 s, and *T* = 1200 s, revealing no significant differences among the results. The scan duration is related to the temporal stability of the random signal of BS and BSWA, and according to a previous analysis,^{21} the measurement duration for the automated scanning measurements was set to 1200 s. For the automated measurements at discrete points, the measurement duration was 180 s for each point.

#### 2. Manual measurements

The manual measurements were performed by both scanning and measurements at discrete points. A specially assembled holder, which could be screwed onto a microphone stand, allowed the simultaneous use of all three probes. The holder can be seen in Fig. 10. This allowed the variation of the surface sampling by using all three probes or only the middle one. The separation between the probes on the holder was 0.24 m.

Contrary to the use of a hemisphere in the automated measurements, the manual measurements were performed over a parallelepiped of varying surface due to the different environmental surroundings.

During the manual measurements, special effort was made to keep the scanning speed lower than 0.5 m/s and as constant as possible, according to the ISO 9614^{11,12} requirements. For the measurements at discrete points, each partial surface was divided into 0.5 m × 0.5 m squares. Using all three probes led to 128 measurement points for the measurements in the hemi-anechoic room, the open space, and the reverberant room and to 78 points for the measurements in the reverberation room. For single probe measurements, the point number is 64 and 26, respectively. Sound intensity was measured for 60 s at each point.

### C. Measured quantities

#### 1. Sound intensity and sound pressure

The sound pressure signals were recorded by a multichannel analyzer, which calculated the auto-spectra and the complex cross-spectra in real time, using a fast Fourier transform (FFT) algorithm with 6401 lines and applying a Hanning window. The spectra were appropriately averaged by the analyzer, depending on the measurement duration, and they were further processed using matlab.

^{22}The spacer length was determined by the finite difference error,

^{23}which is given by

^{24}

Due to the frequency characteristics of the TS and the TSWA input signals, an alternative calculation of the one-third octave bands was applied. In this, only the lines corresponding to the one-third octave band center frequencies and their directly adjacent lines were used (in total three FFT lines for each one-third octave band). The adjacent lines were considered due to the side lobes of the Hanning window applied to the FFT analysis.

#### 2. Pressure-residual intensity index

The pressure-residual intensity index is defined as the difference between the indicated sound pressure level $ L p , \Delta p = 0$ and sound intensity level of the residual intensity $ L I , res$, when the intensity probe is placed and oriented in a sound field whose sound intensity is zero,^{12} using a specially designed coupler. The index is calculated from Eq. (3).

### D. Extraneous noise

In the current state-of-the-art procedures, actions are proposed in case extraneous noise disturbs the sound intensity measurements.^{10–12} To investigate the influence of extraneous noise, a set of measurements was performed in the hemi-anechoic room. A loudspeaker used for facade measurements was utilized as a source of extraneous noise. It was positioned at a corner of the hemi-anechoic room so that it radiated through the measurement surface. The loudspeaker was fed with white noise by a noise generator. Measurements were performed at various noise levels compared to the time and surface-averaged sound pressure level of the source. Measurements were performed with and without noise. For the former, the difference between the level of the source under test and the overall noise level was –10, –5, 0, 5, and 10 dB. The level difference was individually set for each source under test through a graphic equalizer.

An important characteristic of extraneous noise is its stationarity. The measurements included both stationary and non-stationary extraneous noise. The stationary noise measurements were performed while the facade loudspeaker was uninterruptedly emitting during the entire measurement. The non-stationary noise measurements were performed by different configurations depending on the measurement method. For the automated scanning, the measurements were divided into four equal time intervals, and the noise emission was successively switched, e.g., noise—no noise—noise—no noise. For the automated measurements at discrete points, the combination of measurements at different noise levels allowed the non-stationarity of the noise. For half of the points, the measurements without noise were considered, while for the other half, measurements with noise were considered. The same approach was also used for the manual measurements. For the partial surfaces parallel to the facade loudspeaker axis, the measurements without noise were used, while for the partial surfaces perpendicular to the axis, the measurements with noise were used.

### E. Utility of the indicator $ F p I n$

^{10,12}In the theoretical investigation, it was shown that the deviation of the SWL from the actual level is not correlated to this criterion. This was also the case for the measurement results described in Tables I and II (see Appendix). The measurement results were used as follows. The SWLs of all sources for measurements during strong extraneous noise ( $ L p \xaf\u2212 L n=0,\u22125,\u2009and\u221210\u2009dB$) were considered. The deviation from the SWL determined after automated scanning measurements without extraneous noise was set as the related SWL difference using

The SWL differences were checked according to the $ F p I n\u2212 \delta p I 0$ criterion and are presented in Fig. 12 for both values of the bias error factor $K$. It must be noted that for the SWL determination using a single probe, the corresponding $ \delta p I 0$ was used, while for the case of three probes, the lowest value of the three $ \delta p I 0$ was selected for each frequency. The graph reveals no correlation between the two quantities and is, thus, an experimental support to the theoretical findings regarding the redundancy of the unsigned pressure intensity indicator.

### F. Investigation on the required number of measurement points

*C*was 8, which corresponds to survey grade results.

^{10}As previously, the SWL difference was calculated by setting the SWL determined after automated scanning measurements as reference, using

As stated in Sec. IV E, the qualification of the results was performed using the $ F p I n\u2212 \delta p I 0$ criterion of Eq. (8). The SWL difference is shown against the number of minimum points $ N min$ in Fig. 13. Again, a correlation between the SWL difference and the number of the required measurement points is not supported.

## V. CONCLUSION

This paper investigates the use of field indicators for standardized measurements with a p-p sound intensity probe that aim to determine the SWL of a source. In the current ISO 9614 set of standards,^{10–12} the field indicators are used to define criteria to assess the quality of the measured SWL and to decide whether or not a valid result has been obtained. To test the validity of these criteria, analytic calculations of the SWL measured by a p-p sound intensity probe for sources of different order (monopole and dipole), in part superposed by extraneous noise in the form of a plane wave and a diffuse sound field, were performed. These calculations delivered new insights regarding the correlation of the currently used field indicators with the deviation of the measured SWL from the actual SWL.

These theoretical results were confirmed by the results of the experiments, described in Sec. IV. Thus, we conclude that the unsigned pressure intensity indicator $ F p I n$ and the non-homogeneity indicator $ F S$ do not provide any useful information regarding the quality of the measured SWL. We propose to assess the quality of the measured SWLs using solely the signed pressure intensity index $ F p I n$ in combination with the pressure-residual intensity index $ \delta p I 0$. The present research can be the basis for further investigation, which could be used as guidance in a future revision of the whole ISO 9614 set of standards.

A revised and, thus, simplified ISO 9614 set of standards would help machinery manufacturers and other users by reducing the measurement effort for the sound power determination. This, in turn, will improve the reliability of noise emission data of machines and ensure fair competition toward quieter machines. Reliable noise emission data are necessary for employers and users of machines to preferably sell and buy quieter machines (Sell and Buy Quiet). With reliable data, employers can more strategically replace noisy equipment with quieter equipment. Replacing noisy equipment with quieter equipment is one way to better protect their workers from noise.

## ACKNOWLEDGMENTS

Presented results were obtained within a research project undertaken at PTB and funded by the Federal Institute for Occupational Safety and Health (BAuA) as a subproject (F2450) of a focus project aiming at the simplification of noise emission measurement methods. The authors thank Heinrich Bietz for performing measurements at PTB's reverberation room and Kevin Picker for performing a considerable number of the intensity measurements.

## AUTHOR DECLARATION

### Conflict of Interest

The authors have no conflicts to disclose.

## DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

### APPENDIX

## REFERENCES

*Environmental Protection Act 1986*

*The Protection of the Environment Operations (Noise Control) Regulation 2017—Approved Methods for Testing Noise Emissions*

*Handbook of Noise and Vibration Control*

*Noise and Vibration Control Engineering*