Assessing human activity noise in workspaces using machine learning and numerical models

Domenico De Salvio 1 , Giulia Fratoni, Dario D’Orazio, Massimo Garai Department of Industrial Engineering, University of Bologna, Italy Viale del Risorgimento 2, 40136 Bologna, Italy

ABSTRACT Acoustic comfort of workspace environments is deeply dependent on the balance between indoor background noises. For example, colleagues’ speaking might a ff ect task performances by downgrading privacy and productivity. Conversely, HVAC noise can reduce the employee’s distraction since such continuous mechanical noise is detrimental to speech comprehension. Therefore, in the analysis of workspaces’ acoustic comfort, di ff erent background noise sources identification becomes essential. In this regard, machine learning techniques are resourceful for clustering sound pressure level patterns among the unlabeled data. A previous work by the authors provided reliable results on separating noise sources via Gaussian Mixture Model and K-means clustering. Nevertheless, such method was applied to a single workspace, and thus it needs further investigation on a wider sample of environments. For this reason, in the present work long-term monitoring was carried out in various active workspaces extending previous results and confirming the procedure’s robustness. Moreover, simulations of the acoustic conditions by summing up the human activity contribution to the mechanical noise allowed obtaining more reliable speech intelligibility criteria at the workstations. Refining the numerical models’ setup through background noise levels obtained through machine learning analysis enhance the assessment of workers’ privacy condition in realistic scenarios.

1. INTRODUCTION

The comfort of workers deeply depends on their exposure to noise. Concerning this, the recent ISO 22955:2021 focuses its recommendations on the measurement of the ambient noise on workstations. The workers’ exposure is function of the activity carried out within the space. Thus, di ff erent types of activities set di ff erent thresholds to comply with [1]. The background noise is a double-edged sword in o ffi ces. It can either increase or decrease the productivity of employees. The problem depends mainly on intelligibility. The more intelligible the signal is, the more a ff ected are workers’ performances [2]. The other way round, continuous noises disrupt the speech signal, improving the ability to focus. Thus, the ability to discern each sound source within a space becomes very important. Previous work has proposed two procedures to identify the human from the mechanical noise through sound level meter long-term monitoring [3]. Both methods exploit two machine learning algorithms:

1 domenico.desalvio2@unibo.it

a slaty. inter.noise 21-24 AUGUST SCOTTISH EVENT CAMPUS O ¥, ? GLASGOW

Gaussian Mixture Model and K-means clustering. Being based on statistical bases, the chance to use these algorithms is strictly connected to the need for large amounts of data. Hence, the application of the procedures is focused on long-term monitoring. The present work deals with the chance to use two clustering methods and identify di ff erent kinds of noise sources through long-term monitoring. Based on previous study, the analysis is broadened through raytracing simulations to assess the variations of the intelligibility parameters. Moreover, a new parameter arising from Gaussian Mixture Model is introduced to describe the type of activity carried out within the o ffi ces.

2. THEORY AND CONTEXT

The ISO 22955:2021 sets target values of noise for the workstations depending on the kind of activity. Values are reported in Table 1.

Table 1: Target noise levels at workstations L eq , A for each kind of activity according to ISO 22955.

Activity Target values (dBA)

Activity mainly focusing on outside of the room communication 55

Activity mainly based on collaboration between people at the nearest workstation 52

Activity mainly based on a small amount of collaborative work 48

Activity can involve receiving public 55

In this work, three o ffi ces represent the case studies. The activities carried out within are di ff erent in each of them. Following, a brief description of the spaces is presented:

O ffi ce A - Open plan with 8-12 workers. The amount of employees can vary during the day. This is a sales o ffi ce. Hence, the activity is mainly focused on outside of the room communication.

O ffi ce B - Open plan with 10-12 workers. The amount of employees can vary during the day. This is a design o ffi ce. Hence, the activity can be more or less collaborative.

O ffi ce C - Small o ffi ce with a maximum of 2 workers. The amount of employees can vary during the day. The activity carried out has a small amount of collaborative work.

This study was conducted after COVID19. Thus, besides the occupancy’s variations, all o ffi ces were treated with screens 120 cm height.

2.1. Gaussian Mixture Model The Gaussian Mixture Model (GMM) is an iterative method to describe random distributions as a sum of Gaussian curves. It is frequently used as an unsupervised technique in machine learning. The assumption is that all data points are generated from a mixture of Gaussian distributions [4]. The Gaussian probability density function f ( x i ) of a set of observations x 1 , ..., x n can be expressed as a sum of k Gaussian densities f k ( x i , µ k , σ 2 k ):

K X

k = 1 π k f k ( x i , µ k , σ 2 k ) (1)

f ( x i ) ≃

where π k are the mixing proportions [ ? ], non-negative quantities that sum to one; that is,

0 ≤ π k ≤ 1 ( k = 1 , . . . , K )

and K X

k = 1 π k = 1 .

The likelihood function for a mixture model with K univariate Normal components is:

e − ( xi − µ k ) 2

n Y

K X

n Y

K X

k = 1 π k 1 q

2 σ 2 k . (2)

k = 1 π k f k ( x i ) =

L ( x ) =

2 πσ 2 k

i = 1

i = 1

In the present work, the GMM implements the Expectation-Maximization algorithm to fit the original distribution [5].

2.2. K-means clustering The K-means clustering algorithm is an iterative method which aims to minimize the distance among data and clusters. The set of observations x 1 , . . . , x n can be clustered into a set of K clusters, C = { c k ; k = 1 , . . . , K } , where µ k is the mean of cluster c k . In the present work, the distance to minimize is represented by the Euclidean distance. The squared Euclidean distances between µ k and the points in cluster c k is defined as:

J ( c k ) = X

x i ∈ c k || x i − µ k || 2 . (3)

Thus, the aim is to minimize it over all K clusters:

K X

X

x i ∈ c k || x i − µ k || 2 . (4)

J ( C ) =

k = 1

The process ends when the convergence is reached. This is outlined in two steps: first, the optimal partition for a given set of µ k is found; then, the cluster centroids are computed once C is fixed [6]. Figure 1 shows an example of processing for both algorithms. The black solid line on the left represents the probability distribution function obtained by the occurrences of the measured SPLs. The black dashed lines represent the Gaussian curves used to decompose the mixture, four components in this example. On the right, the same distribution is processed via KM and the four clusters are represented in shades of gray.

2.3. The optimal number of clusters One of the issue of many unsupervised techniques concerns the need of specifying the number of clusters to look into the data prior to run the algorithms. There are plenty of techniques to accomplish this task. In this work, the Akaike Information Criterion (AIC) is used to select the optimal number of clusters for GMM and the silhouette coe ffi cient (SC) for KM. The AIC is an informational criterion which rewards the goodness-of-fit of the candidate model penalizing at the same time its complexity [7]. AIC is defined as:

AIC = 2 k − 2 ln [ L ( x )] (5)

where k is the model’s number of parameters and L is the likelihood function defined in previous section. Being the goodness-of-fit evaluated by the negative term, the lowest the AIC the better the model is.

8

0.12

Cluster 1

Cluster 2

0.10

Cluster 3

Occurrence (%)

6

Cluster 4

0.08

Density

4

0.06

0.04

2

0.02

40 50 60 70 80 0

30 40 50 60 70 0

Sound pressure level (dB)

Sound pressure level (dB)

(b) K-means clustering

(a) Gaussian Mixture Model

Figure 1: Data visualizaton of the two algorithms used in the present work: Gaussian Mixture Model on the left, K-means clustering on the right [].

The silhouette coe ffi cient assesses the quality of the assignment of data to each cluster [8]. The mean distance between the data point i and the other points in the same cluster A m is defined as:

a ( i ) = 1 | A m | − 1

X

i , j ∈ A m , i , j d ( i , j ) (6)

where d ( i , j ) is the distance between i and j in the cluster A m . Then, the mean dissimilarity of i with respect to another cluster B n is defined as the mean distance between i and the other data l in B n . Thus, it is possible to define b ( i ) as the shortest distance between i and all the other points in the other clusters: b ( i ) = min 1

X

l ∈ B n , l , i d ( i , l ) . (7)

| B n |

The cluster with the smallest mean dissimilarity is defined as “neighbor" and represents the second- best choice for i . The silhouette value s ( i ) is defined as: 

1 − a ( i ) / b ( i ) if a ( i ) < b ( i ) , 0 if a ( i ) = b ( i ) , b ( i ) / a ( i ) − 1 if a ( i ) > b ( i ) . (8)

Thus − 1 ≤ s ( i ) ≤ 1, which means that i is properly clustered if s ( k ) is near 1, while it is wrongly clustered if s ( i ) is near -1, whereas an s ( i ) near 0 means that i can be assigned to either A or B . Since s ( i ) represents the goodness of the assignment of each data point, the mean of each silhouette value ¯ s ( i ) is used as a metric for the whole clustering process. The SC is finally defined as the highest mean obtained by the candidate models with di ff erent number of clusters k :

SC = max k ¯ s ( k ) (9)

The silhouette coe ffi cient, as well as being one of the most well-known clustering validation indices, is assessed as very viable among di ff erent kinds of datasets [9].

2.4. Measurement and post-processing Two entire days of activity within three di ff erent o ffi ces was measured through a sound level meter. Sound pressure levels (SPLs) were recorded each 0.1 seconds to reach an high resolution monitoring. An acquisition time so short allows to record SPLs even in the pauses among syllables of the speech [10]. About 430k samples for each day were collected in octave bands from 125 to 4000 Hz besides

the global A-weighted average levels. The arrays obtained by the time series represent the database for the application of the two algorithms, GMM and KM. The procedure used in the present study follows the analysis described and proposed in previous work [3]. Thus, the optimal number of cluster is obtained looking at the elbow of the AIC for GMM and the silhouette coe ffi cient for KM. After the best model is picked, the next step labels the sound source as mechanical or human. The means and the standard deviations(SD) for GMM and the centroid and the average intra-cluster distance (AICD) for KM represent the feature used to assign the labels. The logic behind the labeling is based on two assumptions. The first concerns the sound pressure levels of the sources. The mechanical noise should be lower than the speech, indeed. Thus, the lower mean and the lower centroid will be assigned to the mechanical sources. Higher values will be assigned to the human noise. The second assumption regards the variance of the sources’ SPLs source. A mechanical process should measure similar SPLs because of the mechanical cycles, while the speech does not follow always the same rhythm. Thus, lower SD and lower AICD will be assigned to the mechanical sources. Higher values will be assigned to the human noise. Preliminary analyses found a value of SD equal to 5 dB as a good threshold to separate mechanical from human sources [11].

2.5. Numerical models Raytracing simulation allowed the study of the acoustic properties of the o ffi ces. 3D models were created using 3D SketchUp and imported into ODEON Room Acoustic software. The geometry and the modelling pipeline follows the recommendations of the state-of-the-art [12]. All the surfaces were modelled up to the size of 0.35m and the sound absorption coe ffi cients were supplied by scientific literature [12–14]. Since the software describes the sound through rays, the wave nature of the phenomenon is ensured by the introduction of scattering coe ffi cients [15]. The layers were managed dividing the elements with high absorption and scattering coe ffi cients from reflective and smooth elements.

3. RESULTS AND DISCUSSIONS

Numerical models allow to deepen the context analyzing the acoustic properties of the spaces under study. In this work, one or two metrics were used to describe the spaces. For all the o ffi ces the reverberation time T 60 is considered. For the biggest o ffi ces A and B, the spatial decay of the A- weighted level of speech doubling the distance from the source D 2 , S was taken into account also. Following, a brief summary of the simulated parameters:

O ffi ce A - T 60 = 0 . 7 s; D 2 , S = 2 . 4 dB;

O ffi ce B - T 60 = 0 . 7 s; D 2 , S = 3 . 0 dB;

O ffi ce C - T 60 = 1 . 3 s.

Concerning the cluster validation, both AIC curves and silhouette coe ffi cients suggested an optimal number of cluster equal to 2. This means that we can consider the sound context within the measured o ffi ce made by two main sound sources: mechanical (air systems, electronic devices, ...) and human noise (speech). Table 2 shows the results of the clustering analysis carried out over all the o ffi ces. Values are shown for the octave bands from 125 to 4000 Hz and the global A-weighted average levels. The main di ff erence between the two algorithms is due to the kind of clustering that they perform. GMM runs a soft clustering process, i.e. each data point belongs to each cluster according to an assigned probability. Thus, data points can belong to more than one cluster with di ff erent weights [16]. On contrary, KM runs an hard clustering process. Thus, data points can belong to one

(a) O ffi ce A

(b) O ffi ce A

STI 0.8 0.7 0.6 0.5 0.4 Office A 2 3 4 Source-receiver distance (m) @ STI_Inf e@ STI_Mech e@ STI_Hum

(c) O ffi ce B

Figure 2: Overlapping areas for each o ffi ce and each day. Blue Gaussian curves represent mechanical sources, red Gaussian curves represent human sources. The overlapping areas are highlighted in orange.

and only one cluster. As a consequence, the means obtained via GMM are closer than the centroids obtained via KM. Further reason concerning the di ff erence among means and centroids is due to the heteroscedasticity, i.e. the variance of the data. It is well-known that GMM can be considered as a generalization of KM. The two methods give back the same results only if they share the same variance among data [17]. The di ff erences in variances is confirmed by the di ff erences between the means and the centroids of the same source. Mechanical sources show lower di ff erences with respect to the human sources. It is worth noting that human noise obtained via KM have similar values to the A-weighted average levels. Di ff erences are less than 1 dB for the o ffi ce A and B. The o ffi ce C shows di ff erences of 1.3 and 2.2 dB. It can be correlated to the type of activity carried out in this o ffi ce. The small amount of collaborative work can a ff ect the occurrences curve of the human cluster. It is noticeable by the higher AICD measured in this o ffi ce with respect to A and B. Spectral tendencies confirm the type of sources as shown in [3]. Figure 2 shows the decay of the Speech Transmission Index (STI) with respect to the distance. Three curves are shown: the S TI In f without background noise, the S TI Mech considering only the mechanical noise obtained by the clustering, and the S TI Hum considering all the sound sources inside the o ffi ces. The plots show how the ability of separate sound sources provides deeper insights of the spaces under study.

0.8 0.7 STI 0.6 0.5 0.4 Office B @.... e.., e@ STI_Inf e@ STI_Mech STI_Hum 2 4 6 8 10 Source-receiver distance (m)

STI 0.8 0.7 0.6 0.5 0.4 0.5 Office C @ STI_Inf @ STI_Mech STI_Hum 1 1.5 2 2.5 3 Source-receiver distance (m)

Table 2: Results of the clustering carried out over long-term monitoring of the three o ffi ces. The o ffi ce, the correspondent measurement day, the algorithm and the kind of source are shown. Measured SPLs are shown for each octave band from 125 to 4000 Hz, besides the A-weighted values. Moreover, the correspondent A-weighted continuous-equivalent level L Aeq , T measured through the sound level meter is shown.

O ffi ce Day Algorithm Source Frequency octave band A-weighted L Aeq , T 125 Hz 250 Hz 500 Hz 1 kHz 2 kHz 4 kHz

56.5 Human 53.2 (4.3) 52.3 (5.3) 52.6 (8.5) 42.5 (8.6) 37.6 (8.5) 32.6 (8.4) 51.9 (7.7)

55.4 Human 52.9 (4.3) 53.0 (5.6) 51.8 (8.0) 43.4 (8.0) 38.2 (7.7) 32.8 (7.4) 51.8 (7.1)

55.0 Human 49.6 (5.1) 49.3 (6.4) 49.3 (8.3) 44.3 (7.4) 40.2 (7.0) 35.1 (6.8) 50.6 (7.1)

54.5 Human 49.1 (5.0) 48.2 (6.5) 47.9 (8.8) 43.2 (7.7) 39.3 (7.4) 33.6 (6.8) 49.5 (7.5)

53.2 Human 46.1 (7.4) 46.2 (7.5) 45.4 (8.8) 39.6 (8.1) 35.9 (8.3) 29.5 (8.5) 46.3 (7.9)

51.7 Human 43.8 (7.1) 44.1 (7.2) 45.5 (8.8) 38.6 (8.4) 34.7 (8.7) 29.6 (8.2) 45.7 (8.1)

GMM Mechanical 47.7 (1.7) 43.8 (1.4) 37.0 (1.2) 30.3 (1.3) 24.8 (2.3) 19.8 (3.7) 39.8 (1.0)

KM Mechanical 47.8 (1.8) 44.3 (1.9) 38.3 (3.0) 32.5 (3.5) 27.6 (4.2) 22.3 (4.7) 41.3 (2.9)

GMM Mechanical 47.2 (1.7) 43.8 (1.7) 37.7 (1.5) 31.7 (1.8) 26.6 (2.5) 22.3 (3.6) 40.2 (1.4)

KM Mechanical 47.4 (1.8) 44.3 (2.1) 38.9 (3.0) 33.3 (3.3) 28.4 (3.7) 23.3 (3.9) 41.5 (2.8)

GMM Mechanical 40.9 (2.2) 38.7 (2.4) 34.4 (2.2) 33.7 (2.1) 29.8 (2.3) 25.2 (3.1) 38.7 (2.1)

KM Mechanical 41.9 (2.7) 40.1 (3.3) 36.4 (3.9) 35.2 (3.2) 31.7 (3.5) 26.5 (3.6) 40.7 (3.5)

GMM Mechanical 41.7 (1.9) 38.2 (1.9) 33.3 (1.7) 32.7 (1.6) 28.7 (1.9) 23.8 (2.6) 37.9 (1.7)

KM Mechanical 42.3 (2.3) 39.4 (2.9) 35.0 (1.1) 34.0 (3.0) 30.5 (3.2) 25.2 (3.4) 39.5 (3.1)

GMM Mechanical 35.4 (3.2) 35.7 (3.2) 33.8 (4.8) 29.0 (4.2) 22.4 (3.7) 14.2 (1.1) 34.7 (3.5)

KM Mechanical 36.2 (3.6) 36.5 (3.6) 34.2 (4.5) 30.3 (4.4) 25.9 (4.9) 20.6 (4.7) 36.6 (4.3)

GMM Mechanical 34.7 (2.4) 33.5 (2.2) 31.4 (3.8) 27.7 (4.3) 22.0 (4.5) 16.9 (3.0) 33.5 (3.5)

KM Mechanical 35.3 (3.0) 34.5 (3.0) 32.3 (4.2) 28.2 (4.2) 23.6 (4.8) 19.2 (4.3) 34.7 (4.1)

Human 55.5 (3.1) 55.1 (3.9) 57.2 (5.9) 49.6 (6.4) 43.6 (6.4) 37.8 (6.0) 57.0 (5.4)

Human 55.3 (3.1) 55.8 (4.1) 56.4 (5.6) 49.2 (6.0) 43.3 (5.7) 36.9 (5.4) 56.3 (5.1)

Human 52.3 (3.6) 53.0 (4.5) 54.1 (5.8) 49.6 (5.7) 45.2 (5.2) 39.1 (5.0) 55.0 (5.1)

Human 51.8 (3.6) 52.3 (4.8) 53.6 (6.1) 49.3 (6.1) 44.9 (5.7) 37.9 (5.1) 54.6 (5.5)

Human 50.3 (5.3) 50.5 (5.4) 49.8 (6.4) 40.5 (5.7) 41.2 (5.7) 35.7 (5.9) 51.0 (5.7)

Human 48.3 (4.9) 48.8 (5.3) 50.0 (6.4) 43.0 (6.1) 39.7 (6.2) 34.8 (6.0) 50.4 (5.9)

B 1

B 2

C 1

C 2

A 1

A 2

Table 3: Results of the overlapping areas OvA for each combination of o ffi ce and day. Values are shown for each octave band from 125 to 4000 Hz and the overall A-weighted average level.

O ffi ce - Day Octave band

125 Hz 250 Hz 500 Hz 1 kHz 2 kHz 4 kHz LeqA

A - 1 0.307 0.154 0.067 0.119 0.179 0.256 0.086

A - 2 0.286 0.166 0.098 0.164 0.212 0.310 0.115

B - 1 0.208 0.194 0.122 0.203 0.216 0.291 0.158

B - 2 0.244 0.187 0.113 0.172 0.186 0.256 0.144

C - 1 0.277 0.288 0.365 0.365 0.232 0.082 0.276

C - 2 0.272 0.208 0.233 0.357 0.309 0.218 0.263

4. OVERLAPPING AREAS

The main di ff erence between GMM and KM is the definition of soft and hard clustering. The first kind of algorithms, like GMM, assign data points to each cluster with a probability weight. Thus, each data point can belong to many clusters. The other way round, hard clustering algorithms force the assignment of each data point to one and only one cluster CIT. Thus, GMM can have overlapped areas among the components, i.e. the Gaussian curves. Under the assumption that the mechanical component does not change during long-term monitoring, it may be deduced that the overlapped area depends by the speech component. Thus, it depends on the extent of the collaboration among workers. On the basis of these considerations, the overlapping value (OvA) of the two components is proposed as the metric to assess the amount of collaboration among employees according to the ISO 22955. Measuring the overlapping areas between clusters is an important issue in the machine learning field. Hence, several algorithms were proposed [18,19]. In the present work, the OvA value lies in the range [0,1]. OvA is equal to 0 when the two Gaussians do not have any overlapping and is equal to 1 when the two components are the same, i.e. totally overlapped. Table 3 shows the results obtained by the evaluation of the OvA. The values achieved for the average A-weighted levels show small di ff erences between the days of each o ffi ce but large di ff erences among the case studies. Both results seem reasonable. The activity inside the space can vary day by day but globally, the fluctuations remain in small intervals. At the same time, the o ffi ces show di ff erent average OvAs. This results may be influenced by the number of workers in the o ffi ce besides the collaboration among them. O ffi ces A and B, both containing an average of 10 people, show a similar scale of values. This does not happen in o ffi ce C that contain 2 people at most. Figure 3 shows the plots of the components obtained via GMM. The considerations made above can be visualized here. The overlapping areas are highlighted in orange. Blue and red lines indicate respectively the mechanical and the human sources.

5. CONCLUSIONS

The separation of sound sources inside an o ffi ce is an important issue to assess the workers’ comfort. The present work exploits machine learning algorithms to separate the active classes of sounds in three o ffi ces during working hours. The procedure is the same described in previous works by the authors. A sound level meter recorded the entire working day in three o ffi ces for two di ff erent days. Then, clustering analyses via Gaussian Mixture Model and K-means were carried out. Features like standard deviation and the average intra-cluster distance allow to label the class of

(a) O ffi ce A - Day 1

(b) O ffi ce A - Day 2

‘Aysueq

(c) O ffi ce B - Day 1

(d) O ffi ce B - Day 2

or

(e) O ffi ce C - Day 1

(f) O ffi ce C - Day 2

Figure 3: Overlapping areas for each o ffi ce and each day. Blue Gaussian curves represent mechanical sources, red Gaussian curves represent human sources. The overlapping areas are highlighted in orange.

rr a

the sound sources. Results confirm the ability of these algorithms to separate the di ff erent sources. Measurements were compared with the A-weighted average continuous level. K-means provides results more similar to the continuous levels. Numerical models were used as tool to investigate the acoustic context of the measurement. The modelling process followed the state-of-the-art and gave back reliable results about the reverberation time for all the o ffi ces and the spatial decay of the speech levels for the biggest spaces. Moreover, the spatial decay of the Speech Transmission Index was evaluated through raytracing simulations in three di ff erent conditions: with no background noise, with only the mechanical noise, and with all the active sources obtained by the clustering analyses. Under the assumption of a constant mechanical noise, Gaussian Mixture Model can provide a tool to assess the collaboration among employees according to ISO 22955. This tool is represented by the measurement of the overlapping areas between the two Gaussian curves. Results show how the ability of separating noise source in real-world conditions can return more deep insights about the acoustic context really experienced by people. Further studies will focus on broadening the analyses in di ff erent type of o ffi ces to reach better understanding about the acoustic of workplaces.

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