Error and Uncertainty in Near-Field Sound Power Assessments of In- dustrial Sources Jon Tofts Environment Agency Rivers House, Bridgwater, Somerset, TA3 5LA. UK 1. INTRODUCTION

Near-field sound pressure measurements may be converted into sound power levels (L w ) in order to populate propagation models. Although standards exist such as ISO 3740:2019 1 which present rig- orous methods for the accurate determination of sound power levels, complying with such standards is not always feasible once an industry is operational. In such cases, it is common to see propagation models populated using a sound power estimate from a single field-based measurement.

Alternatively, propagation models can be populated using sound power data that have been pro- vided by equipment manufacturers or that have been presented in other standards such as BS 5228- 1:2009+A1:2014 2 .

Previous papers commonly consider the uncertainty associated with laboratory-based sound power assessments 3 . This paper will explore the sources of error and uncertainty within near-field sound power estimates from field-based sound pressure levels, and suggest ways to minimise them.

2. DISTANCE

Sound power levels can be derived from sound pressure levels using equation (1):

𝐿 𝑝 = 𝐿 𝑊 −10𝐿𝑜𝑔 ൬ 𝑄

4𝜋𝑟 2 ൰ (1)

Where: L P = Sound pressure level L W = Sound power level Q = Directivity (1 is a source radiating into a full sphere, 2 is a hemisphere etc) r = Distance to source (m) The distance to the source, r, is critical to the accurate assessment of the sound power level. In the field, this measurement would be made using a tape measure or with a laser range-finder. However, in practice, it is difficult to assess the exact distance to a noise source when the source is comprised of multiple individual sub-sources.

For example, Figure 1 is a photo taken during a near-field measurement at a waste processing industry that was the focus of a noise impact assessment submitted to the UK Environment Agency. The description of the measurement was:

130 LCN Excavator with grab loading container 10m distance Leq: 69.5dB(A) 4:22 min measurement duration L W 97.5dB(A)

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Figure 1: 130 LCN Excavator with grab loading container Rearranging equation (1) to result in the derivation of sound power from sound pressure results in equation (2):

𝐿 𝑝 + 10𝐿𝑜𝑔 ൬ 𝑄

4𝜋𝑟 2 ൰= 𝐿 𝑊 (2)

Substituting the submitted measurement data shows how the sound power level of 97.5dB(A) L W was derived using equation (2):

69.5 + 10𝐿𝑜𝑔 ൬ 2 4𝜋10 2 ൰= 97.5dB(A) (3)

One issue with this measurement is that there are multiple sub-sources within this single operation, all of which are at different distances. These include the excavator engine, the engine exhaust, the grab claw, the hydraulic pump, and the material handling noise.

It is not possible to calculate a standard uncertainty associated with the distance to these individual sub-sources, however, it could be estimated that at a worst case, these sub-sources could be between 6m for the nearest material handling noise source and 12m for the most distant exhaust noise source. Most of the sub-sources would likely be within 1m of the stated 10m distance.

The distance based sound power error from a 10m measurement distance is presented in Figure 2:

3

2

1

dB (Lw) error

0

-3.0 -2.0 -1.0 0.0 1.0 2.0

Distance error (m)

-1

-2

-3

Figure 2: Distance based L w error from a 10m measurement

The potential error associated with distance error increases as the measurement distance reduces (a - 1m error for a measurement taken at 5m is greater than a -1m error for a measurement taken at 20m). This is shown in Figure 3:

7.0

6.0

5.0

Lw Error (dB)

4.0

3.0

2.0

1.0

0.0

0 2 4 6 8 10 12 14 16 18 20

Meaurement distance -1m (m)

Figure 3: Lw error associated with a -1m measurement error at a range of measurement distances

Using 10m ±1m presents a realistic upper and lower boundary for the potential error of this example using equations (4) and (5):

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69.5 + 10𝐿𝑜𝑔൬ 2 4𝜋9 2 ൰= 96.6dB(A) (4)

69.5 + 10𝐿𝑜𝑔 ൬ 2 4𝜋11 2 ൰= 98.3dB(A) (5)

When compared to the submitted sound power level of 97.5dB(A) L w , this potential 1m uncertainty presents a realistic error range of +0.8dB(A) to -0.9dB(A). 3. DIRECTIVITY

The directivity (Q) in equation (1) assumes uniform radiation into a hemisphere over a reflective surface. This is clearly not what is presented in Figure 1. Not only does the ground surface have a varying reflectivity, but the dominant noise sources (the engine exhaust) does not radiate uniformly.

NANR174 4 presented a 95% confidence interval of ±1.5dB(A) across a 10m hemispherical meas- urement of a dynamic front loader and ±2.6dB at the dominant engine frequency while stationary. This is a useful benchmark for the directivity of similar heavy equipment. 4. OPERATING DURATION

Noise propagation models submitted to the Environment Agency will typically be used to inform a noise impact assessment using BS 4142 5 , which requires the impact to be assessed over a (daytime) reference time interval of 1 hour. If the sound source is operating for less than the reference time interval, the level should be time corrected to an equivalent level over one hour. Additionally, an 8 hour working day is also commonly constructed.

It is possible for site operators to generalise the duration of each sound source. If the true operating duration was 30 minutes rather than 1 hour, this would result in a -3dB error when corrected to a 1 hour reference time interval. Alternatively, if the duration was 1 hour ± 30 minutes within an 8 hour working day then this would result in a +1.7dB to -3dB potential error. In addition to these quantifiable errors, there are other potential sources of error that can only be estimated: 5. OPERATOR DIFFERENCES

Although hard to quantify, it is very likely that site operators will behave differently when they know they are being monitored (the ‘Observer Effect’), particularly when the monitoring is being performed for the purposes of regulation and compliance. Operators may use a lower engine power or handle material more carefully when being observed. The uncertainty associated with this behaviour cannot be quantified, but is likely to fall within a range of ±5dB(A).

6. HANDLING DIFFERENT MATERIALS

In the case presented in Figure 1, the material being handled appears to be light domestic waste with a high proportion of plastic. This material will be quieter to handle than heavier waste with a higher proportion of glass or metals. The single 4 minute measurement is unlikely to adequately represent a

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full range of materials, and this results in an additional source of uncertainty. This cannot be quanti- fied, but is likely to fall within a range of ±2dB(A).

7. OTHER SOUND SOURCES

Although the microphone seen in Figure 1 is pointed towards the sound source being investigated, the microphone itself is designed to be close to omnidirectional. This means that other sound sources within the acoustic environment may be contributing to the measured level. Given that the sound under investigation should be dominant within the acoustic environment, the error associated with other sources is likely to fall within the range of ±1dB(A).

8. PUBLISHED SOUND POWER LEVELS

A common alternative to near-field measurements is to populate a sound propagation model with sound power data supplied by the equipment manufacturer, or with data from (for example) BS 5228.

It is extremely unlikely that an equipment manufacturer will be able to supply sound power data that satisfies the requirements of ISO 3740, and that has consideration of source directivity while under typical load (in this case, waste handling). The standardised equipment data presented in BS 5228 also has no consideration of source directivity and may not be directly equivalent to the opera- tion under investigation. 9. OVERALL ERROR AND UNCERTAINTY

These sources of error and uncertainty are summarised in Table 1.

Table 1: Summarised sources of uncertainty

Source of error Error type Potential positive error

Potential negative error Distance

0.8dB(A) 0.9dB(A) Directivity 1.5dB(A) 1.5dB(A) Operating Duration 1.7dB(A) 3dB(A) Operator differences

Quantifiable

5dB(A) 5dB(A) Different materials 2dB(A) 2dB(A) Other sound sources 1dB(A) 1dB(A) Although the potential worst case error falls within the range of +12dB(A) to -13.4dB(A), this is not a standardised uncertainty that can be quantified in this way. There is no measure of the likelihood of any of these events occurring, and, from the perspective of an acoustician, it would be prudent to place more effort in minimising such uncertainties rather than quantifying them. This is also the ap- proach recommended by BS 4142, the UK Environment Agency 6 and by Craven and Kerry 7 .

Estimated

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10. MINIMISING ERROR AND UNCERTAINTY

Each of these potential sources of error and uncertainty can be minimised.

• Careful distance measurement to the dominant sound source can reduce the distance error, but cannot remove the complication of multiple sub-sources. • The error associated with source directivity can be minimised by measuring on the propagation pathway to the intended receptor, or by measuring in multiple directions around the sound source. • The potential error of inaccurate operating times can be minimised by the equipment operator keeping detailed logbooks of the use of each piece of equipment. • Operator differences is harder to minimise but can be reduced by the operator following a strict operating procedure. • The varying noise from the handling of different materials can be minimised by measuring a full range of materials being handled. • The impact of other sound sources within the acoustic environment can be minimised by en- suring that they are turned off. 11. CONCLUSION

This paper has considered the potential sources of uncertainty associated with near-field sound power measurements made of industrial sources. Isolating, identifying, and attempting to quantify these un- certainties shows that the potential errors associated with the near-field measurement of sound power levels is considerable.. However, with careful planning each source of error can be minimised and can result in a more acceptable level of overall uncertainty.

12. REFERENCES 1 ISO 3740:2019 “Acoustics – Determination of sound power levels of noise sources – Guidelines

for the use of basic standards” 2 BS 5228-1:2009+A1:2014 “Code of practice for noise and vibration control on construction and

open sites – Part 1: Noise” 3 “Measurement uncertainties in the sound power procedures based on sound intensity” Carletti and

Pedrielli, ICSV13 Vienna , 2006 4 NANR174 “Construction noise database (phase 3): Evaluation of established measurement proto-

col” Waddington and Moorhouse , University of Salford , 2006 5 BS 4142:2014+A1:2019 “Methods for rating and assessing industrial and commercial sound” 6 “Guidance – Noise and vibration management: Environmental Permits”, July 2021. Joint guidance

by Environment Agency, Natural Resources Wales, Scottish Environment Protection Agency and Northern Ireland Environment Agency 7 A good practice guide on the sources and magnitude of uncertainty arising in the practical meas-

urement of environmental noise” Craven and Kerry, University of Salford, 2007

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