Evaluating the specific sound level from plant and machinery in high residual sound environments Matt Torjussen 1 ANV Measurement Systems Beaufort Court, 17 Roebuck Way, Milton Keynes, MK5 8HL

ABSTRACT BS 4142 requires the selection of periods within a sound pressure level time series to calculate the specific sound level from the ambient and residual sound levels. This is usually done in the time domain by monitoring and/or controlling the specific sound source(s); however, there are instances where it is necessary to evaluate the specific sound level at a remote location without any control over the operation of the specific sound source(s), which may make it difficult to obtain a representative specific sound level where there are high levels of residual sound. BS 4142 directs practitioners to carry out measurements closer to the source and then use a calculation method to estimate the specific sound level at the assessment location(s). For some types of specific sound sources, it may be possible to increase the accuracy of the specific sound level evaluation using two microphones. This paper presents a method that uses two microphones to acquire ambient sound data simultaneously at the receptor and closer to the source. Magnitude squared coherence is used to identify the components present in the signal measured at the receptor that are also present in the signal measured closer to the source. This approach allows the specific sound level to be evaluated when the difference between the overall A-weighted ambient and residual sound levels is less than 3dB. 1. INTRODUCTION

British Standard 4142:2014 (“BS 4142”) [1] provides methods for assessing the degree of impact that industrial and commercial sound has on residential receivers. The assessment uses a noise intrusion model: the relative difference between the rating level (the sound of the industrial or commercial specific source plus certain acoustic feature corrections) and the background sound level in the absence of the specific sound. The greater the excess of the rating level over the background sound level, the greater the likelihood of adverse impact.

Measuring, evaluating, and assessing sound from specific industrial and commercial sound sources is made difficult by the presence of other residual sound sources such as road traffic noise. BS4142 requires that residual sound be minimised such that the ambient sound containing the specific sound is greater than 3dB above the residual sound. Such minimisation is done by measuring at times and during intervals when the residual sound has subsided to low levels. A combination of measurement and calculation may be used when this is not possible; for example, measuring closer to the source and then using a calculation method to estimate the specific sound level at the assessment location. Where a specific sound source cannot be turned off, it is also permissible to determine residual and background sound levels at an alternative location deemed representative by the environmental noise practitioner.

1 matt@anv.uk.com

For small-scale residential planning applications, the specific industrial and commercial sound may be at a low level relative to the residual sound but, due to acoustic features, could still be audible and require assessment. However, it is not always possible to control the source or get close enough to characterise it sufficiently to make calculations possible.

The problem is best illustrated using example A2 from BS 4142 itself. In this example a factory is emitting continuous hums which are not significantly in excess of the residual sound at the assessment location. The ambient sound level is 40dB L Aeq,20mins and the residual sound level is 35dB L Aeq,20mins . Using energy subtraction, the resulting specific sound level is 38dB(A).

In real assessments it is commonly the case that the ambient sound level is very close to the residual sound level, if not the same overall level. This is particularly so in urban areas where new residential development is proposed close to restaurants and retail premises but also near other residual sound sources. A planning application for residential development may also be controversial in such situations, which can make it difficult to elicit the co-operation from the owner/operator of the specific sound source to control it for the purposes of a noise assessment.

Where the residual sound level is very close to the specific sound level it can be useful to contrast the random nature of the residual sources with the ordered nature of sound from fixed plant by analysing them in the frequency domain [2].

2. AN ALTERNATIVE APPROACH

Where the residual sound level is close to the ambient sound level, BS4142 recommends determining a measured attenuation function based on the ambient sound level measured at the assessment location, L a , and a level measured at a reference location, L r , closer to the source. The ambient sound level at the assessment location can be described using the system network illustrated in Figure 1 [ ibid. ].

Figure 1: System network that is subject to analysis

Most modern Class 1 compliant sound level meters have a sampling frequency, f s , of 48kHz. This high time resolution contains detailed information about the specific industrial and commercial sound sources that is lost when it is integrated (in the case of the integrated-averaged ambient sound) or decimated (in the case of the exponentially-averaged background sound) into longer periods. Using the full-time resolution of the sound level meter it is possible to separate the specific and residual sound sources using methods commonly employed in the telecommunications, audio and automotive industries for source separation and noise suppression [3].

2.1. Signal Processing The transfer function can be calculated if the full 48kHz time series is preserved, which can give high-frequency resolution whilst retaining phase information. To illustrate the usefulness of retaining 100% of the data collected by a sound level meter, two recordings have been made of a group of air source heat pumps, one at a distance of 4m from the closest item of plant and another at 20m. The time series for the recordings have been presented in Figure 2 and they may be listened to by scanning the QR codes. The specific sound of the heat pumps is dominant in the reference recording. In the recording made at the assessment location, the tonal sound from the heat pump is audible but residual road traffic noise dominates.

> Beterence Recording, ri) Propagation + Ambient Sound Recording ‘Sound Source Residual Sound @ Assessment Location, a(t)

Figure 2: Time series of (a) the ambient sound measured at the assessment location 20m from the

source, and (b) a reference signal measured 4m from the source.

For high resolution audio recordings made at the assessment location, a(t) , and at the reference location, r(t) , the transfer function, H ra (f) , is [see 2]:

𝐻 𝑟𝑎 (𝑓) = 𝑃 𝑟𝑎 (𝑓)

𝑃 𝑎𝑎 (𝑓) (1)

where the power spectrum, P aa (f) , is [see 2] :

𝑃 𝑎𝑎 (𝑓) = 𝐹𝐹𝑇{𝑎(𝑡)} ∙𝐹𝐹𝑇 ∗ {𝑎(𝑡)}

2 (2)

𝑁 𝑓𝑓𝑡

and the cross-power spectrum, P ra (f) as [see 2] :

𝑃 𝑟𝑎 (𝑓) = 𝐹𝐹𝑇{𝑎(𝑡)} ∙𝐹𝐹𝑇 ∗ {𝑟(𝑡)}

2 (3)

𝑁 𝑓𝑓𝑡

N fft is the number of samples included in the fft calculation.

The spectral estimation assumes that the signals are stationary. For fixed mechanical plant this may be an acceptable assumption; but this is not the case for the residual sound, which included non- stationary road traffic noise. Heavily overlapped time windows containing 4096 samples were used to mitigate this, over which time the signal could be assumed to be stationary.

The magnitude squared coherence function can be used as a measure of the quality of the transfer function and shows how well (or badly) the reference signal correlates with the signal measured at the assessment location. From the coherence function, both excessive noise and causality can be identified. The magnitude coherence function, C ra (f) , is computed as [see 2]:

𝐶 𝑟𝑎 (𝑓) = |𝑃 𝑟𝑎 (𝑓)| 2

𝑃 𝑎𝑎 (𝑓) ∙𝑃 𝑟𝑟 (𝑓) (4)

The result of the magnitude squared coherence function is a value between zero and one versus frequency, with zero indicating no correlation and one indicating 100% correlation between the measurements made at the reference position and the assessment location for a given frequency line. For the example signals presented in Figure 2, the magnitude squared coherence is shown in Figure 3.

Figure 3: Magnitude squared coherence calculated between r(t) and a(t) .

It is clear from the magnitude squared coherence that the tonal components of the air source heat pumps are the parts of the spectrum that show the highest correlation between the reference recording and the recording made at the assessment location. This corresponds with the elements of the specific sound that are audible in the recording made at the assessment location.

2.3. Spectral Subtraction & Auralisation Once causality has been established using the magnitude squared coherence function, an estimate of the specific sound at the assessment location, s est (t) , may then recovered using [see 3]:

𝑠 𝑒𝑠𝑡 (𝑡) = 𝑖𝑓𝑓𝑡{𝐻 𝑎𝑟 (𝑓) ∙𝐹𝐹𝑇{𝑎(𝑡)}} (5)

The specific sound level can be calculated from the resulting de-noised signal, which may also be played back as audio for the practitioner to experience what the specific sound is like with the residual sound significantly attenuated. The estimated specific sound recording has been presented as a spectrogram against those of the reference recording and the ambient sound recording at the assessment location in Figure 4.

(a) L r = 62dB L Aeq

(b) L a = 56dB L Aeq

(c) L s,est = 51dB L Aeq

Figure 4: Spectrograms of (a) reference recording (b) the ambient sound at the assessment location

and (c) the estimated specific sound level with the residual sound significantly attenuated. The spectrograms were created using 7/8 th overlapped Hann windowed data containing 4096 samples.

Scan the QR codes with your mobile device to listen to the recordings used to create these

spectrograms.

The resulting specific sound level is 5dB below the ambient sound level; however, the most heavily contributing frequency lines of the specific sound would have obeyed the 3dB rule from BS4142.

3. SUMMARY & CONCLUSIONS

Signal processing techniques commonly implemented in the telecommunications, audio and automotive industries have been used to attenuate the residual sound in an ambient sound recording containing industrial and commercial sound. These techniques are readily implementable where two sound level meters are available with wave recording capabilities and allow an environmental noise practitioner to: • accurately compute the transfer function between a reference and assessment location in narrow bands; • attenuate residual sound that is dominant in the ambient sound at the assessment location; and, • auralise the specific industrial and commercial sound that is being assessed with minimal residual sound. As well as its use in BS4142 assessments, removing residual sound from audio recordings in this way also has a useful application in soundscaping. With sufficient reference channels, individual sound sources may be isolated from a complicated soundscape for experimental re-mixing and objective evaluation.

Further work is likely to include deriving specific sound from ambient sound recordings using blind source separation, i.e., where there is no reference signal. 4. REFERENCES

1. British Standards Institute (BSI), Methods for Rating and Assessing Industrial and Commercial

Sound , BSI, BS 4142:2014+A1:2019 Edition. 2. Cerna, M. & Harvey, A. F. The Fundamentals of FFT Based Signal Analysis and Measurement ,

National Instruments, 1 st Edition, 2000. 3. Smith, S. W. The Scientist and Engineer's Guide to Digital Signal Processing , 1st Edition,

California Technical Pub, 1997.