Measuring and identifying background noises in offices during work hours
Dario D’ORAZIO(1) , Elena ROSSI(2) , Domenico DE SALVIO(3) , Massimo GARAI(4)(1) University of Bologna, Italy, dario.dorazio@unibo.it(2) University of Bologna, Italy, elena.rossi56@unibo.it(3) University of Bologna, Italy, domenico.desalvio2@unibo.it(4) University of Bologna, Italy, massimo.garai@unibo.it

Abstract
Acoustical comfort inside open-plan offices is necessary for optimal work performance. In fact, it is well known
that productivity is closely related to the acoustic conditions of the working environment. Noise inside offices
is basically due to two kinds of sources: mechanical sources (HVAC devices, office equipment like printers,
phones, etc.) and human activities (human activity noise). The combined effect of these noise sources may
play a key role in privacy metrics, e.g. the STI and its spatial decay. Therefore some technique is needed to
identify and separate the contribution of each kind of source. The data for the present work are a set of short-Leq
values acquired over long-term sound pressure levels recordings. Noise sources are identified using a two-stepstatistical technique: at first the blind Gaussian Mixture Model (GMM) is used to segment the sources, theneach source is classified using a customary statistical analysis. It is shown that the probability distribution ofeach source can be identified, conferring a different sound pressure level to each one. In order to investigate thedynamic behaviour of privacy criteria, these analyses are carried out for each octave band frequency.
Keywords:open plan office, background noise, source separation

1

INTRODUCTION

Acoustic comfort in offices is an important aspect to provide a high level of productivity and quality of work.
Background noise is an important factor influencing privacy in offices and it can be seen as the most importantparameter for the acoustical office design[1]. Colle and Welsh highlighted that distraction in the work placeis not strictly related to the sound pressure level but to the speech intelligibility value [2]. Thus, if the noise
carries information, like the speech from neighbors in the office, there’s a lack of productivity [3]. The speech
intelligibility is defined in IEC 60268-16 [4] by the Speech Transmission Index (STI). It depends on the acoustical conditions of the room and the background noise. The calculation of this criterion can be adjusted in
post processing selecting a more specific background noise condition, so the measurement of the latter is very
important. Since noise reduces speech intelligibility of other people’s communications, it can be considered asa fundamental criterion to improve the work flow. For this reason, the background noise should be neither
too low nor too high [5]. ISO 3382-3 [6] specifies the parameters which describe the acoustical state like the
distraction distance (rD ) and the spatial decay rate of speech per distance doubling (D2,S ). All these parameters are connected to the noise sources, so analyzing them means understanding how the acoustic conditions
influence the comfort. The sound field in an enclosed space is different if it is in the occupied or unoccupied
state so a sound source could have more than one behavior. In addition, in the occupied state there are further
sound sources, i.e. the equipment and the human activities. In the project phase of an open plan office, theability to distinguish between sources of a different nature is important to suggest specific interventions. The
background noise (LB ) due to HVAC could be controlled by interventions on single devices, whereas the humanactivity noise (LS ) could be influenced by LB and by the distance from the devices, that contribute to trigger
the Lombard effect [7].
Hodgson et al. [8] suggested a method to measure the background noise into classrooms with a statisticaltechnique, differentiating the student activity during lecture from the speech level of the speaker. Dehlbæk et2460

al. [9] applied this method in order to measure the human activity noise in open-plan offices. Measuring for awhole working day with a sound level meter, the occupied and unoccupied state of an office can be analyzed.
Basic statistical techniques find out the most common SPLs. Iterative statistical algorithms permit to pointout the sound levels attributable to the various sources in the office. In the present work, noise sources are
identified using a two-step statistical technique: at first the blind Gaussian Mixture Model (GMM) is used tosegment the sources, then each source is classified using a customary statistical analysis. It is shown that theprobability distribution of each source can be identified, conferring a different sound pressure level to each one.
In order to investigate the dynamic behavior of privacy criteria, these analyses are carried out for each octave
band frequency. This newer technique is compared with the standard percentile levels technique to evaluate thebackground noise.

2

STATISTICS OF SOUND PRESSURE LEVELS

100
90

8
Cumulative distribution

75
50
25
0
30

40
70
50
60
Sound pressure level (dB)(a) Percentile Levels TechniqueOccurrences distribution
Gaussian distributions

Percentile level L90

Occurrence (%)

Percentage o f exceeded time (%)

A statistical analysis of the data collected by a sound level meter, distributes the sound pressure levels basing
on their occurrences. In this way it is possible to highlight the most frequent levels during the work day. If
the frequency (in the statistical sense) of a sound pressure level is high, it means that there is a sound source
working at that level continuously.

6
4
2
0
30

40
70
50
60
Sound pressure level (dB)(b) Gaussian Mixture

Figure 1. Two statistical methods used in the present work. In figure (a) the continuous line represent the
cumulative distribution of the recorded SPL of a sound level meter. In figure (b) the continuous line represents
the occurrences distribution of the same measurement. The asymmetrical distribution was decomposed in four
Gaussian curves. The mean values of Gaussian curves indicated with * correspond to the sound sources.
Studying the occurrences in each octave band is useful to distinguish the kind of sound source which is operating. Two statistical methods were used for the survey: percentile levels (PL) and Gaussian Mixture Model(GMM).
Regarding the percentile, it is worth remembering that in statistics, the rank r of a percentile q of N observations
is defined as:qr(q) =(N + 1)(1)
100Consequently, the value of the acoustic percentile level Lq of a certain dataset is equal to the rank r of 100-q.
For a large number of observations, if the occurrence curve is represented by f (x), the value q can be expressed

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as:

Z ∞

q = P(x > Lq ) =f (x)dx.

(2)r(100−q)

Gaussian Mixture Model decomposes the original model data in a sum of gaussian curves. The clusters, represented by the gaussian curves, and their points are defined via Maximum Likelihood method. With Rstudio [10]is possible estimate via Expectation - Maximization (EM) [11] iterative algorithm the Maximum Likelihood of
the recorded SPL.
Let X be a set of independent observations, x1 , . . . , xn , drawn from a mixture of Gaussian distributions; thedensity f (xi ) can be written in the formKf (xi ; ψ) = ∑ πk fk (xi ; θk ) i = 1, . . . , n,

ψ = {θ , π}

(3)

k=1

where the fk (xi , θ )s are the Gaussian densities with parameter vector θk = {µk , σk2 ; k = 1, . . . , K} and πk are theso called mixing proportions, non-negative quantities that sum to one; that is, 0 ≤ πk ≤ 1 (k = 1, . . . , K) and∑Kk=1 πk = 1 [12]. The likelihood function for a mixture model with K univariate Normal components is:
n

K

n

K

2

1

(x −µ )
− i 2ke
L (ψ|x) = ∏ ∑ πk fk (xi |θk ) = ∏ ∑ πk √2πσ 2i=1 k=1i=1 k=1

2σ
k

.

(4)

Detailed information on the samples collected can then be obtained through statistical analysis. Three successive
steps of analysis are identified: the distribution of the occurrences of the measured SPL, for each octave band
(125 Hz - 4000 Hz), the segmentation of the occurrences in Gaussian curves as possible sources constituting thebackground noise and finally the identification of human (LS ) and mechanical (LB ) contribution (figure 2).

3

METHOD

A small open-plan office, with four workplaces, was used as case study in this preliminary study (figure 5).
Sound pressure levels were recorded for an entire work day with a sound level meter with 0.1 seconds ofsample time for acquisition. The sample population was hypothesized large enough to identify Gaussian curves.
For the GMM method the algorithm was set as "random", which means that the number of the Gaussian curves
was calculated automatically in order to optimize the fit. The number of Gaussian curves obtained and thecorresponding standard deviation were extracted. The standard deviation (s.d.) permits to identify the natureof the source: if the s.d. is low (say < 5 dB) it belongs to a mechanical sources, if it is greater (≥ 5 dB) it
belongs to human activities. In this study a s.d. value of 5 dB is considered the threshold to discern the typeof source according to the literature [13, 14, 15]. Afterwards, the sound pressure levels of the office have been
calculated using the diffuse field formula:
4
LP,S,i = LW,S,i + 10log − 11A(5)where LW,S is the sound power level of (normal) speech as the ISO 3382-2 [6] suggests, A is the equivalent
absorbent area of the room and i = (1, ..., 6) represent the range of octave band from 125 Hz to 4000 Hz. To
verify the tendency of the sound pressure levels of the human activity noise, the measured values have been
compared with the calculated ones. Leq and the percentile level L90 were extracted as the standard procedures
require. This analysis was conducted for each octave band from 125 Hz to 4000 Hz.

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Measurements[xn ]iPERCENTILETECHNIQUE
Segmentation,
Identification

PROPOSEDALGORITHM
Segmentation

LS,i = Leq
LB,i = L90[S j , ..., Sm ]i

Identification
Analysis of
σ [S j ]i

If σ < 5

If σ ≥ 5
Spectral matching with
LP = LW,S + 10 log(4/A) − 11YesLS,i = µi [Sm ]i

Noµi [S j ]i

10
LB,i = ∑m−1
j=1 10Figure 2. Step of the analysis made by Percentile Levels and made by Gaussian Mixture Model. i = (1, ..., 6)
is the range of the octave band (125Hz - 4000Hz) and S j = (1, ..., m) are the noise sources individuated by the
proposed algorithm (EM algorithm in this study). In this study S j = (1, ..., m − 1) are assumed as mechanicalsources and Sm is assumed as human activity source.

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4

RESULTSThe results for the two techniques are shown in table 1 for the percentile levels method and in table 2 for theGaussian Mixture Model analysis. In table 2, for the GMM technique, the human activity source is in boldstyle. In figure 3 the mean values of the GMM analysis are plotted in function of the standard deviation, foreach octave band. The means corresponding to the mechanical noise (in black) are distribute in the left part,with s.d less than 4 dB and LP values between 15–45 dB, with little differences between them. The means of
the human noise (in white) with a s.d. grater than 6 dB and LP values greater than 35 dB, represent outliers
from the others values.
Table 1. Identification and segmentation of Leq and L90 (in dB) with percentile levels technique.
Percentile level (dB)
Mechanical
Human activity

L90
Leq

Frequency octave band (Hz)
125

250

500

1000

2000

4000

29.5
32.6

26.7
34.1

23.7
36.2

19.9
30.1

17.5
24.6

20.7
20.3

Table 2. Identification of the possible sound sources and segmentation into mechanical and human noise with
GMM technique. The means and the standard deviations (s.d.) are shown.
Sound level of the n-th
segmented noise source

Frequency octave band (Hz)

(dB)

125

250

500

1000

2000

4000

1
2
3
4
5
6
7
8
9

–
–
–
–
–
–
31.1 (1.9)
34.6 (3.3)
44.2 (6.9)–––
26.8 (1.4)
28.5 (1.0)
30.5 (1.0)
32.9 (1.4)
36.2 (2.6)
45.2 (6.8)––
23.5 (1.2)
25.7 (1.1)
27.9 (1.0)
30.2 (1.1)
33.1 (1.7)
37.1 (2.9)
46.3 (7.9)–––
19.7 (1.0)
21.3 (0.8)
23.1 (1.1)
25.9 (1.9)
31.2 (3.9)
39.0 (8.3)

17.2 (0.4)
17.9 (0.3)
18.6 (0.4)
19.6 (0.6)
21.1 (0.9)
23.2 (1.2)
26.3 (1.7)
30.4 (3.0)
35.8 (7.1)

19.0 (0.4)
20.8 (0.3)
21.2 (0.2)
21.7 (0.2)
22.1 (0.3)
22.8 (0.7)
24.4 (1.6)
27.9 (3.2)
34.2 (6.0)

33.3
39.0

33.3
35.8

32.4
34.2

Levels’ sum of sources
Mechanical
Human activity

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36.2
44.2

39.3
45.2

39.7
46.3

50

45

45

45

40

40

40

35
30
25
20
15

Means (dB)50

Means (dB)Means (dB)

50

35
30
25
20

0

15

2
4
8 10
6
Standard deviation (dB)

30
25
20

0

15

2
4
8 10
6
Standard deviation (dB)(a) 125 Hz

50

45

45

45

40

40

40

30
25
20

Means (dB)

50

35

35
30
25
20

0

15

2
4
8 10
6
Standard deviation (dB)

2
4
8 10
6
Standard deviation (dB)(c) 500 Hz

50

15

0

(b) 250 Hz

Means (dB)Means (dB)

35

35
30
25
20

0

(d) 1000 Hz

2
4
8 10
6
Standard deviation (dB)(e) 2000 Hz

15

0

2
4
8 10
6
Standard deviation (dB)(f) 4000 Hz

Figure 3. Relationship between means obtained by the GMM clustering and the standard deviation for eachoctave band.

50

Lp (dB)

45
40
35
30

LS meas.
LP calc.

125

250 500 1000 2000 4000
Frequency (Hz)Figure 4. Spectral matching between the measured values of the noise source hypothesized as human anddiffuse speech level in the room under study (equation 5).

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Figure 5. Layout of the office with the position of the sound level meter.

5

DISCUSSIONS

The more complex statistical approach with the Gaussian Mixture Model allows to highlight every sound sourcein an enclosed space regardless of its nature, mechanical or human. Results show how GMM brings back morevalues than PL. The random algorithm permits to extract a certain number of clusters, thereafter the distance
between the means and their standard deviations can be re-conducted to a specific kind of noise source. Little
differences between the means could be connected to the same source while a tiny standard deviation indicatesthe mechanical nature of the source. In fact, a little standard deviation means that a source produces a specificsound pressure level continuously during time. Quite the opposite, a high standard deviation means a more
accidental nature of the source, like the human activity. The comparison between the mean values identified as
human source and the diffuse speech levels characteristic of the office under study shows the same trend withdifferences of up to 4 dB. This result confirm, with good approximation, the threshold chosen for the standard
deviation and it could be implemented, for a more accurate similarity, with a neural network. Thus GMM isa stronger method than the percentile levels one, since, in order to obtain the same results with this latter, isnecessary to know the percentage of exceeded time for each noise source.

6

CONCLUSIONS

Identifying sound sources in a work space is an important aspect in order to attain a high acoustical comfort
and improve the productivity. This study compares two statistical techniques to highlight their differences indistinguishing the various sources. The percentile levels technique is a standard method of analysis; it is usedhere for comparison with the Gaussian Mixture Model, which represents a newer approach to the statistical dataobtained by a sound level meter. This latter method allows to identify not only the number of noise sources inthe space but their nature too. In fact, properly using the standard deviation it is possible to identify the kindof source: if the s.d. is high then the source works in a larger range of sound pressure levels, thus it can’t beconsidered as mechanical source but more random like the human activity. This approach of analysis allows apotential deeper understanding of the acoustical field in an enclosed space in order to operate more accurately
in the correction of the criteria which describe the acoustical quality of the space, e.g. the STI, and the designinterventions to achieve a better comfort of the work flow.

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