Assessment of outdoor-to-indoor noise attenuation levels for night-time residential noise exposure

Abstract

Although people spend most of their night-time hours indoors, environmental noise exposure is typically assessed using outdoor levels. This study examined outdoor-to-indoor noise attenuation across 49 dwellings in Greater London using synchronized and unsupervised measurements, while noise levels were expressed via the A-weighted equivalent ( $L_{Aeq}$ ), maximum ( $L_{Amax}$ ), and percentile ( $L_{A01}$ , $L_{A05}$ , $L_{A10}$ ) noise indicators. Moderate-to-strong correlations between night-time outdoor levels and outdoor-to-indoor attenuation levels ( $r=0.4$ – $0.8$ ) informed the development of multiple and mixed-effect linear regression models to estimate indoor noise levels based on outdoor levels. Mixed-effect models outperformed multiple linear models (RMSE: 0.7–4.9 vs 2.3–5.7 dB(A)), with outdoor levels accounting for most variability, and with additional contributions from the occupation status, window size, and room volume predictors. The estimated attenuation levels ranged from 20 to 26 dB(A), with $L_{Aeq}$ in line with the WHO recommended 25 dB(A) level. The proposed modeling approach enables estimates of indoor noise exposure, offering a more representative basis for night-time exposure–response assessments in the UK and similar urban settings.

Introduction

Environmental noise exposure has been associated with negative impacts on human health, such as annoyance,^1,2 quality-of-life,^3,4 and various cardiometabolic outcomes.^5,6 In children, continuous noise exposure may present detrimental and irreversible effects on mental development. ⁷ Regarding night-time residential noise exposure, significant associations have been identified with various aspects of sleep, ⁶ as well as with health-related outcomes and overall quality of life.^8,9 During sleep activity, people not only perceive and evaluate various sound stimuli but also react to them (e.g. stress reaction, awaking episode, and motility reaction). ¹⁰ In children, sleep can be characterized as important, ¹¹ considering the impact of sleep quality on cognitive performance. ¹²

Various noise indicators have been proposed for the quantification of noise exposure. ¹³ However, most studies focusing on children’s noise exposure rely primarily on “traditional” energy-based metrics, such as the A-weighted equivalent ( $L_{Aeq}$ ) and the day-evening-night ( $L_{den}$ ) noise indicator. ¹⁴ In contrast, relatively few studies incorporate alternative indicators, including percentile (e.g. $L_{A01}$ ) or maximum ( $L_{Amax}$ ) noise indicator. ¹⁴ While $L_{Aeq}$ is commonly used to characterize night-time noise exposure, typically assessed over the period from 23:00 to 07:00, it may not fully capture the impact of individual noise events. In this context, the $L_{Amax}$ indicator is recommended for evaluating discrete noise events in sleep-related studies.^15,16 Supporting this approach, the WHO advises that both the number of noise events and their respective sound levels should be considered in night-time exposure assessments. ¹⁷

Noise exposure studies are typically conducted using outdoor noise exposure levels rather than the levels transmitted indoors from external noise sources. ¹⁴ Particularly, outdoor exposure levels are often treated as proxies for indoor exposure levels, reflecting a challenging assumption. ¹⁸ Consequently, there is a need to develop approaches that estimate the attenuation of noise from outdoors to indoors, enabling the estimation of indoor noise exposure levels from outdoor data (e.g. noise maps). A critical factor in this attenuation process is the building façade, including its components (e.g. wall or window structures), which plays a major role in sound transmission. ¹⁴ Among façade components, windows are the most significant pathways for sound energy transmission indoors. ¹⁹ The position of the window, whether open, tilted, or closed, significantly influences the amount of sound transmitted indoors, with the most notable variability observed between buildings when the windows are closed. ²⁰ Indoor (room) acoustic characteristics, particularly reverberation time, also impact the level of attenuation from outdoor to indoor environments. Yet, current statistical approaches have not incorporated such room acoustics predictors. ¹⁴

The objective of this study is to investigate the difference between outdoor and indoor night-time residential noise exposure levels, utilizing sound level data obtained through an unsupervised measurement methodology. Although such methodologies are frequently applied in environmental noise monitoring, they present challenges in the accurate representation of indoor acoustic environments and their correspondence outdoor levels, indicating the need of applying a proper post-processing methodology. To characterize outdoor-to-indoor noise attenuation, statistical regression models were developed, facilitating the estimation of indoor exposure from outdoor measurements. Finally, this approach is intended to support epidemiological evidence of noise-induced health effects associated with outdoor-based indoor noise exposure levels.

Regarding the structure of this study, this consists of two main components. First, a methodological framework was established to integrate valid synchronized and unsupervised indoor and outdoor measurements, accounting for the influence of dominant indoor noise sources and background noise levels, to estimate outdoor-to-indoor attenuation levels. This was based on experimental data collected from 49 dwellings in Greater London, UK. Second, statistical models, including multiple and mixed-effect linear regression, were developed to predict attenuation levels using a variety of noise indicators. These models incorporated predictors from three domains: the outdoor environment (e.g. noise levels and source type), the indoor environment (e.g. room size and occupation status), and the building façade structure (e.g. window size and type).

Methodology

Selected measurement sites

Residential buildings located in the Greater London area of the United Kingdom and close to major roads, railway, and under aircraft paths of Heathrow or London City airports were selected for the conduction of outdoor and indoor noise exposure measurements. ²¹ Additionally, a site survey was conducted to record the type of sound sources present in each of the selected locations. Particularly, the sites were exposed to various residential noise sources, with road traffic noise constituting the primary source of disturbance (33%), and secondary exposure to a combination of aircraft, road, and rail traffic (67%), occurring during the autumn (10%), winter (51%), spring (31%), and summer (8%) seasons. It is important to note that the considered rooms were located at the ground-floor with the windows kept closed during the measurement process. In residential façade structures, 82% of the dwellings were equipped with multi-layered windows, while the remaining 18% were fitted with single-layered windows. Finally, the window structures cover surface areas ranging from 0.75 to 11.3  $m^2$ , and the volumes of the rooms range from 9.88 to 70.7  $m^3$ .

Study invitations were disseminated via email to Imperial College London staff and students, with the objective of recruiting participants for the study. Some of the participants were identified through existing connections with the Heathrow Association for the Control of Aircraft Noise (HACAN). It was ensured that the selected locations were residential (furnished) dwelling rooms (bedrooms) with at least one window (facing the street). During the noise measurements, all the windows were kept closed in the chosen rooms, ensuring consistent environmental conditions. Noise measurements with open and tilted windows were therefore not conducted. However, it should be noted that opening windows for ventilation or the operation of mechanical ventilation systems may be required in practice. This may result in a significant impact to indoor noise levels. ²²

The suitability of setting up the monitoring system (indoor and outdoor noise sensors) in optimal positions was verified in collaboration with the enrolled participants. The minimum distance between the outdoor and indoor sensors, the security of the equipment, and the avoidance of placing the equipment near heating or air-conditioning units was ensured. In accordance with the aforementioned criteria, out of the 67 dwellings that were evaluated, 49 met the selection criteria. The dwellings included were a mix of terraced houses (45%), mid-rise flats (14%), high-rise flats (19%), semi-detached houses (10%), and detached houses (12%). Most dwellings had two (30.6%) and three occupants (28.6%), followed by those with one occupant (24.5%). A smaller proportion of dwellings housed four occupants (6.1%), while five and 6 occupants each accounted for 4.1% of the sample. One unoccupied dwelling (2.0%) was also included in the measurement campaign. The measurement campaign obtained approval from the Imperial College Research Ethics Committee, Joint Research Compliance Office (ICREC Reference: 16IC3545).

Measurement campaign

Unsupervised and time synchronized outdoor and indoor noise exposure measurements were conducted in accordance with British Standard ²³ for almost three consecutive days at each location between December 2016 and August 2017, using a measurement integration time of 1 min. In particular, outdoor noise exposure measurements were taken at a distance of at least 1 m from the most exposed façade, 3.5 m from other reflecting surfaces, and at a height of 1.5 m from the ground. None of the selected locations feature obstacles such as balconies, which could have potentially obstructed the outdoor levels. Similarly, indoor noise exposure measurements were taken in furnished rooms at a distance of at least 1 m from the main window and at a height of 1.5 m from the floor. Although noise measurements were conducted for almost three consecutive days, ²¹ our study focused solely on measurements during the night-time period (23:00–07:00), as the background noise levels are lower in comparison to day-time and evening period. In this way, the outdoor-to-indoor noise attenuation levels can be evaluated in a representative way using the applied unsupervised measurement methodology. No individuals were present in the selected rooms during the noise measurements.

Regarding the measurement equipment, a Class 1 sound level meter (Optimus CR: 171B) was placed inside and outside with an outdoor measurement kit (Optimus CK: 670) for the outdoor measurements. Prior to measurements, each sound level meter was gaged by the manufacturer. Furthermore, an acoustic calibrator (Optimus CR: 51) was employed for the calibration of sound level meters on-site prior to the commencement of each measurement. It should be noted that audio recordings during the course of measurements were not undertaken in accordance with the terms of the ethical committee approval agreement.

Regarding the noise exposure assessment in both indoor and outdoor environments, average noise levels were calculated over 1-h and 8-h intervals during the night-time period, defined as 23:00–07:00. In particular, the 1-h interval during the night-time period is associated with the hour ranges of 23:00–00:00, 00:00–01:00, 01:00–02:00, 02:00–03:00, 03:00–04:00, 04:00–05:00, 05:00–06:00, and 06:00–07:00, while the 8-h interval is associated with the whole night hours of 23:00–07:00. The two-studied intervals were selected to facilitate a comparison of the impact of the finer resolution (1-h) with that of the coarser resolution (8-h). Finally, the noise levels were expressed via the objective noise indicators; A-weighted equivalent ( $L_{Aeq}$ ), maximum ( $L_{Amax}$ ), and percentile ( $L_{A01}$ , $L_{A05}$ , $L_{A10}$ , and $L_{A99}$ ), using the NoiseTool software. ²⁴

In addition to noise measurements, supplementary data were collected on the outdoor and indoor environments, as well as building characteristics at each location, including: window size ( $m^2$ ), room volume ( $m^3$ ), window type (single-layered or multi-layered glazing), site type (single-exposure of road traffic or multi-exposure of combined road, rail, and air traffic) and occupation status (occupied or non-occupied). However, additional information related to the façade structure, such as the type of wall, the materials, year of construction/renovation, were not collected during the measurement campaign.

Processing of noise exposure measurements

To assess the sound insulation of façade structures, outdoor and indoor acoustic measurements are typically conducted under controlled conditions, following criteria that account for both recorded sound levels and (indoor) background noise, ensuring accurate representation of outdoor and indoor sound levels.^25–27 According to these standards, frequency-dependent outdoor noise levels should exceed the corresponding indoor levels, and indoor levels should surpass background noise by at least 6 dB(A), and preferably 10 dB(A). These conditions ensure that background noise does not distort the evaluation of façade sound insulation.

As an unsupervised (uncontrolled) approach was employed to assess outdoor-to-indoor attenuation levels, dominant indoor sources and background noise levels may have violated the conditions typically required in controlled settings for accurately capturing attenuation levels.^26,27 Therefore, a processing methodology was applied. Initially, outdoor-to-indoor level differences were calculated for equivalent, maximum, and percentile ( $N=01$ , 05, and 10) noise indicators across each time interval. Only data (outdoor and indoor levels) with positive differences were retained, as negative values indicate that indoor noise levels, likely from dominant internal sources, exceeded outdoor levels, thus compromising attenuation assessment.

An evaluation procedure was implemented to account for the contribution of indoor background noise to the measured indoor levels. To assess background noise, percentile noise indicators such as $L_{A90}$ and $L_{A95}$ are employed to describe typical ambient noise levels, while $L_{A99}$ is often used to estimate the underlying noise floor. ²⁸ These background percentile indicators were therefore considered to characterize indoor background conditions. A recent study using the same dataset found no significant differences in the Pearson correlation coefficient between outdoor-to-indoor level differences and outdoor levels when using these indicators, supporting the use of $L_{A99}$ as a representative measure of night-time indoor background noise. ²⁹ Accordingly, outdoor-to-indoor level differences were considered valid only when the indoor equivalent levels ( $L_{Aeq}$ ) exceeded the background noise levels ( $L_{A99}$ ) by at least 6 dB(A) or 10 dB(A), representing lower and higher thresholds for indoor background noise influence, respectively. Both indoor and corresponding outdoor levels were excluded when difference between indoor and estimated background noise levels failed to meet the two thresholds. These conditions were applied solely to the equivalent noise indicator. For maximum and percentile indicators ( $N=01$ , 05, 10), which capture peak and intermittent events, the indoor levels were at least 10 dB(A) larger in relation to the indoor background noise expressed via the $L_{A99}$ noise indicator. Therefore, the analyses were only conducted with respect to the two time-interval steps (1-h and 8-h).

Statistical analyses

To evaluate and model the impact of various predictors on the outdoor-to-indoor noise level difference, both multiple (MLRMs) and mixed-effect linear regression models (MELRMs) were developed using Jamovi 2 software, ³⁰ following established statistical modeling approaches. ³¹

The analysis considered both continuous and categorical predictors. The continuous predictors included outdoor noise levels ( $L_{Ai,Out}$ ), window size, and room volume. The two-level categorical predictors included window type (single-layered and multi-layered), site type (road-traffic and multi-exposure), and occupation status (occupied and unoccupied). The outcome (response) variable was the outdoor-to-indoor level difference, $\Delta L_{Ai,Out-In}$ , where $i$ denotes the type of noise indicator under under the specified time intervals and indoor background noise conditions. In particular, for the equivalent noise indicator, the regression modeling was performed across the two background noise conditions (6 and 10 dB(A)) and two time intervals (1-h and 8-h). For the maximum and percentile noise indicators, the regression modeling was carried out for the two time intervals only.

Initially, the relationship between outdoor noise levels and the outdoor-to-indoor level differences was explored using the Pearson correlation coefficient ( $r$ ). ³² The correlation strength is classified as: weak ( $0.20\le r<0.40$ ), moderate ( $0.40\le r<0.60$ ), strong ( $0.60\le r<0.80$ ), and very strong ( $0.80\le r\le 1$ ). ²¹ Furthermore, the cumulative probability distribution (CPD) functions ³³ of the measured outdoor-to-indoor level differences, expressed using the applied noise indicators, were calculated for central outdoor noise exposure levels ranging from 40 to 90 dB(A), with grouping windows of ± 5 dB(A) around each central outdoor level.

In multiple linear regression models, the predictors were selected using a stepwise elimination process, beginning with a full model that included all predictors and removing non-significant ones in each step ( $p>0.05$ ). ANOVA was employed to confirm the statistical significance of the retained predictors ( $p\le 0.05$ ). The normality of residuals was evaluated using the Kolmogorov-Smirnov test for samples with $n\ge 50$ and the Shapiro-Wilk test for $n<50$ , where $n$ is the number of observations. ³⁴ Outliers were identified using Cook’s distance, ³⁵ while multi-collinearity among predictors was assessed using the Variance Inflation Factor (VIF), retaining variables with VIF < 5. ³⁶ To assess the risk of false-positive correlations ( ${\beta }_{error}$ ), the models were also fitted on standardized versions of the dataset. ³⁷ Furthermore, the Wald t-distribution approximation was used to compute 95% Confidence Intervals (CIs) and $p$ -values. ³⁸ The modeling performance was reported using both $R^2$ and adjusted $R^2$ ( $R_{adj}^2$ ) metric, where the latter account for the number of predictors and provide an unbiased estimate of variance explained. ³⁹ Moreover, the relative importance of each predictor, defined as its contribution to the explained variance, was quantified using the Lindeman, Merenda, and Gold (LMG) method. ⁴⁰

In mixed-effect linear regression models, an approach similar to the multiple linear regression models was followed for estimating the $\Delta L_{Ai,Out-In}$ . Additionally, a random intercept was included for each location ID (1–49) to account for repeated measures of noise exposure within the same dwelling, following the established methodology and diagnostics for mixed-effect modeling. In particular, the $R_M^2$ metric was used for quantifying the performance of the mixed-effect linear regression models in terms of the proportion of variance explained by the fixed effects and the total variance. ⁴¹ The mixed-effect linear regression models were developed using the restricted maximum likelihood (REML) estimator and optimized using the BOBYQA algorithm. ⁴² Similar to the multiple linear regression models, the relative contribution of fixed predictors to the $R_M^2$ metric was also evaluated. ⁴³

Finally, the evaluation of both modeling approaches was conducted in RStudio using a 10-fold cross-validation procedure. ⁴⁴ In this approach, the dataset was randomly partitioned into 10 (non-overlapping) folds of approximately equal size. In each iteration, approximately 90% of the data were used to refit the model and estimate the regression coefficients, while the remaining 10% were kept for validation. This process was repeated 10 times, ensuring that each data subset was used exactly once for testing. The predictive performance of the model was assessed by averaging the root mean squared error (RMSE) across all folds. The RMSE, which represents the standard deviation of the residuals, quantifies the average error between the predicted and observed $\Delta L_{Ai,Out-In}$ levels.

Regression modeling

Both multiple and mixed-effect linear regression models were developed to express the outdoor-to-indoor level difference in terms of the significant predictors for each time interval, background noise condition, and noise indicator. In equations (1)–(12), the multiple linear regression models are summarized per noise indicator.

• – Models based on the $L_{Aeq}$ noise indicator:

$$\Delta L_{Aeq,1h,06dB,Out-In}={\beta }_0+{\beta }_1{L}_{Aeq,1h,06dB,Out}+ST+{\beta }_{2}WS+OS+{\beta }_{3}RV$$

(1)

$$\Delta L_{Aeq,1h,10dB,Out-In}={\beta }_0+{\beta }_1{L}_{Aeq,1h,10dB,Out}+ST+{\beta }_{2}WS+OS$$

(2)

$$\Delta L_{Aeq,8h,06dB,Out-In}={\beta }_0+{\beta }_1{L}_{Aeq,8h,06dB,Out}+ST+WT+OS$$

(3)

$$\Delta L_{Aeq,8h,10dB,Out-In}={\beta }_0+{\beta }_1{L}_{Aeq,8h,10dB,Out}+ST+{\beta }_{2}WS+OS.$$

(4)

• – Models based on the $L_{Amax}$ noise indicator:

$$\Delta L_{Amax,1h,Out-In}={\beta }_0+{\beta }_1{L}_{Amax,1h,Out}+ST+WT+OS$$

(5)

$$\Delta L_{Amax,8h,Out-In}={\beta }_0+{\beta }_1{L}_{Amax,8h,Out}+ST+OS.$$

(6)

• – Models based on the $L_{A01}$ noise indicator:

$$\Delta L_{A01,1h,Out-In}={\beta }_0+{\beta }_1{L}_{A01,1h,Out}+ST+{\beta }_{2}WS+WT+OS$$

(7)

$$\Delta L_{A01,8h,Out-In}={\beta }_0+{\beta }_1{L}_{A01,8h,Out}+OS.$$

(8)

• – Models based on the $L_{A05}$ noise indicator:

$$\Delta L_{A05,1h,Out-In}={\beta }_0+{\beta }_1{L}_{A05,1h,Out}+ST+WT+OS$$

(9)

$$\Delta L_{A05,8h,Out-In}={\beta }_0+{\beta }_1{L}_{A05,8h,Out}+ST+WT+OS.$$

(10)

• – Models based on the $L_{A10}$ noise indicator:

$$\Delta L_{A10,1h,Out-In}={\beta }_0+{\beta }_1{L}_{A10,1h,Out}+ST+WT+OS$$

(11)

$$\Delta L_{A10,8h,Out-In}={\beta }_0+{\beta }_1{L}_{A10,8h,Out}+ST+WT+OS.$$

(12)

In these models, ${\beta }_0\in ℝ$ denotes the intercept, ${\beta }_1\in ℝ$ denotes the coefficient (estimate) for the equivalent, maximum, and percentile regression models which express the outdoor noise exposure predictor, ${\beta }_2\in ℝ$ denotes the coefficient for the window size (WS) predictor, and ${\beta }_3\in ℝ$ denotes the coefficient for the room volume (RV) predictor. Site type (ST), window type (WT), and occupation status (OS) denote the two-level categorical factor predictors, where the level 1 corresponds to the reference level.

Similarly, in equations (13)–(24), the mixed-effect linear regression models are summarized per noise indicator, where ID  $\in \{1,\dots ,N\}$ denotes the measurement locations, and $(1|ID)$ introduces a location-specific random intercept.

• – Models based on the $L_{Aeq}$ noise indicator:

$$\Delta L_{Aeq,1h,06dB,Out-In}={\beta }_0+{\beta }_1{L}_{Aeq,1h,06dB,Out}+OS+\left(1|ID\right)$$

(13)

$$\Delta L_{Aeq,1h,10dB,Out-In}={\beta }_0+{\beta }_1{L}_{Aeq,1h,10dB,Out}+{\beta }_{3}RV+\left(1|ID\right)$$

(14)

$$\Delta L_{Aeq,8h,06dB,Out-In}={\beta }_0+{\beta }_1{L}_{Aeq,8h,06dB,Out}+{\beta }_{3}RV+\left(1|ID\right)$$

(15)

$$\Delta L_{Aeq,8h,10dB,Out-In}={\beta }_0+{\beta }_1{L}_{Aeq,8h,10dB,Out}+{\beta }_{2}WS+\left(1|ID\right).$$

(16)

• – Models based on the $L_{Amax}$ noise indicator:

$$\Delta L_{Amax,1h,Out-In}={\beta }_0+{\beta }_1{L}_{Amax,1h,Out}+OS+\left(1|ID\right)$$

(17)

$$\Delta L_{Amax,8h,Out-In}={\beta }_0+{\beta }_1{L}_{Amax,8h,Out}+OS+\left(1|ID\right).$$

(18)

• – Models based on the $L_{A01}$ noise indicator:

$$\Delta L_{A01,1h,Out-In}={\beta }_0+{\beta }_1{L}_{A01,1h,Out}+OS+\left(1|ID\right)$$

(19)

$$\Delta L_{A01,8h,Out-In}={\beta }_0+{\beta }_1{L}_{A01,8h,Out}+\left(1|ID\right).$$

(20)

• – Models based on the $L_{A05}$ noise indicator:

$$\Delta L_{A05,1h,Out-In}={\beta }_0+{\beta }_1{L}_{A05,1h,Out}+OS+\left(1|ID\right)$$

(21)

$$\Delta L_{A05,8h,Out-In}={\beta }_0+{\beta }_1{L}_{A05,8h,Out}+\left(1|ID\right).$$

(22)

• – Models based on the $L_{A10}$ noise indicator:

$$\Delta L_{A10,1h,Out-In}={\beta }_0+{\beta }_1{L}_{A10,1h,Out}+OS+\left(1|ID\right)$$

(23)

$$\Delta L_{A10,8h,Out-In}={\beta }_0+{\beta }_1{L}_{A10,8h,Out}+\left(1|ID\right).$$

(24)

Results

Assessment of outdoor levels and outdoor-to-indoor level differences

After processing the night-time data based on the $L_{Aeq}$ indicator, a total of 371 outdoor and indoor level pairs were valid for the 1-h time interval and 161 pairs for the 8-h time interval under the 6 dB(A) background noise condition. Similarly, a total of 109 pairs for the 1-h interval and 59 pairs for the 8-h interval were valid under the 10 dB(A) background noise condition. Figure 1 presents the boxplots of the equivalent outdoor ( $L_{Aeq,Out}$ ) and outdoor-to-indoor ( $\Delta L_{Aeq,Out-In}$ ) levels, while in Table 1, their descriptive statistics are summarized. As seen from Figure 1 (top) and Table 1, the range of outdoor noise levels is smaller for the 8-h time interval than for the 1-h time interval for both indoor background noise conditions. In addition, the variability in the indoor levels, corresponding to impact of façade characteristics, was responsible for the presented outdoor-to-indoor level ranges in Figure 1 (bottom). Both the level ranges and mean levels were reduced by increasing the background noise condition from 6 to 10 dB(A) in both time intervals, indicating the impact of indoor background noise levels over the stricter condition. Overall, there was a mean difference of approximately 22 and 21 dB(A) in outdoor-to-indoor levels regarding the 6 and 10 dB(A) background noise condition in both time intervals, respectively.

Figure 1.

Assessment of outdoor levels (top) and outdoor-to-indoor level differences (bottom) expressed via the $L_{Aeq}$ noise indicator per background noise condition (BGN: 6 and 10 dB(A)) and time interval (1 and 8 h). The horizontal line and asterisk denote the median and mean level, respectively.

Table 1.

Descriptive statistics of outdoor levels and outdoor-to-indoor level differences per noise indicator with respect to background noise condition and time interval.

Indicator (dB(A))	Mean	Std	Median	IQR: 25%	IQR: 75%	Min	Max	Range
$L_{Aeq,1h,6dB,Out}$	55.4	6.9	56.1	50.7	61.5	38.6	69.1	30.5
$L_{Aeq,1h,10dB,Out}$	58.1	5.9	58.6	53.4	63.7	43.6	69.2	25.6
$L_{Aeq,8h,6dB,Out}$	54.1	6.0	53.6	50.0	58.3	43.0	66.2	23.2
$L_{Aeq,8h,10dB,Out}$	56.5	6.0	56.4	52.8	63.1	43.0	66.2	23.2
$L_{Amax,1h,Out}$	65.9	9.9	66.6	59.4	74.2	42.4	96.2	53.8
$L_{A01,1h,Out}$	57.9	10.0	58.5	51.7	67.0	37.3	82.8	45.5
$L_{A05,1h,Out}$	52.6	9.8	53.3	45.7	43.4	33.5	74.4	40.9
$L_{A10,1h,Out}$	50.5	9.7	51.0	43.4	58.5	31.9	73.1	41.2
$L_{Amax,8h,Out}$	75.2	7.9	74.2	70.1	80.7	57.9	96.2	38.3
$L_{A01,8h,Out}$	63.0	7.8	64.0	57.9	70.1	46.7	82.3	35.6
$L_{A05,8h,Out}$	56.6	7.5	57.2	52.8	61.6	42.3	71.0	28.7
$L_{A10,8h,Out}$	53.3	7.6	53.7	48.5	57.3	40.1	69.1	29.0
$\Delta L_{Aeq,1h,6dB,Out-In}$	22.9	6.5	24.0	20.0	27.6	8.5	39.5	31.0
$\Delta L_{Aeq,1h,10dB,Out-In}$	21.0	6.7	22.5	17.6	26.4	9.8	39.5	29.7
$\Delta L_{Aeq,8h,6dB,Out-In}$	22.4	6.1	24.1	20.7	26.9	5.0	37.9	32.9
$\Delta L_{Aeq,8h,10dB,Out-In}$	21.3	6.8	22.7	19.7	26.2	5.0	37.9	32.9
$\Delta L_{Amax,1h,Out-In}$	22.0	7.8	23.7	18.5	28.4	4.1	47.3	43.2
$\Delta L_{A01,1h,Out-In}$	23.1	6.6	24.6	19.0	28.4	7.5	41.4	33.9
$\Delta L_{A05,1h,Out-In}$	23.8	5.8	24.3	20.0	28.2	9.4	39.7	30.3
$\Delta L_{A10,1h,Out-In}$	23.8	6.6	24.4	20.0	28.4	8.6	45.0	36.4
$\Delta L_{Amax,8h,Out-In}$	17.6	9.5	18.9	11.3	25.0	2.5	53.7	51.2
$\Delta L_{A01,8h,Out-In}$	23.9	6.9	24.5	20.2	28.5	8.6	43.6	35.0
$\Delta L_{A05,8h,Out-In}$	24.4	6.7	25.9	21.2	29.3	9.5	45.5	36.0
$\Delta L_{A10,8h,Out-In}$	25.1	6.2	25.8	21.6	29.0	11.4	45.0	33.6

IQR: inter-quartile range; Std: standard deviation.

As regards the noise exposure levels expressed using the maximum ( $L_{Amax}$ ) and percentile ( $L_{A01}$ , $L_{A05}$ , and $L_{A10}$ ) noise indicators, a total of 907 and 151 outdoor and indoor level pairs were valid for the 1-h and 8-h time intervals, respectively. Figure 2 presents the boxplots of outdoor and outdoor-to-indoor noise levels expressed via the maximum and percentile noise indicators, while the descriptive statistics of the presented boxplots are also included into Table 1. As seen from Figure 2 (top), the ranges of outdoor noise exposure levels expressed via the maximum and percentile noise indicators present similar trends to those depicted by the equivalent noise indicator by increasing the time interval step from 1-h to 8-h. Focusing on their outdoor-to-indoor level differences in Figure 2 (bottom), the level difference based the on $L_{Amax}$ indicator presented the greatest level range. As the $L_{Amax}$ indicator reflects the most dominant noise events, it is associated with the highest degree of variability. In contrast to $L_{Amax}$ , the percentile noise indicators $L_{A01}$ , $L_{A05}$ , and $L_{A10}$ , which characterize strong acoustic events, show reduced variability and increased mean level difference at lower percentile thresholds. For different indicators and time intervals, the mean outdoor-to-indoor levels ranging from 19 to 26 dB(A) were obtained.

Figure 2.

Assessment of outdoor levels (top) and outdoor-to-indoor level differences (bottom) expressed via the $L_{Amax}$ , $L_{A01}$ , $L_{A05}$ , and $L_{A10}$ noise indicators per time interval (Time: 1 and 8-h). The horizontal line and asterisk denote the median and mean level, respectively.

The relationships between the equivalent outdoor-to-indoor level differences ( $\Delta L_{Aeq,Out-In}$ ) and outdoor ( $L_{Aeq,Out}$ ) levels were explored via the Pearson correlation coefficient ( $r$ ) with respect to both background noise conditions and time intervals, and the results are presented in Figure 3 (top). As it can be seen, the explored relationships exhibited a higher degree of correlations in the 10 dB(A) background noise condition (1-h: $r=0.71$ and 8-h: $r=0.54$ ) compared with the 6 dB(A) background noise condition (1-h: $r=0.63$ and 8-h: $r=0.49$ ). This indicates the significant influence of the indoor background noise on the outdoor-to-indoor level differences. As a consequence, the more stringent background noise criterion of 10 dB(A) was favored over the less stringent criterion of 6 dB(A). With respect to the temporal resolution, the examined relationships exhibited stronger correlations in the 1-h temporal resolution than in the 8-h temporal resolution. This suggests that a high time resolution (1-h) can be beneficial compared with a low time resolution (8-h) and moreover, the latter resolution requires a greater number of measurements for capturing reliable noise exposure levels.

Figure 3.

Relationship between outdoor levels and outdoor-to-indoor level differences expressed using (top) $L_{Aeq}$ noise indicator with respect to background noise condition (BGN), as well as (mid-left) $L_{Amax}$ , (mid-right) $L_{.0A01}$ , (bottom-left) $L_{A05}$ , and (bottom-right) $L_{A10}$ noise indicators per time interval (time).

Similar to the equivalent noise indicator, the relationships between the outdoor noise levels and outdoor-to-indoor level differences expressed through the maximum ( $L_{Amax}$ ) and percentile ( $L_{A01}$ , $L_{A05}$ , and $L_{A10}$ ) noise indicators were explored, using the Pearson correlation coefficient. The explored relationships are presented in Figure 3 (mid and bottom). As it can be seen, the correlation coefficient for the percentile noise indicators exhibited varying degrees of strength, from moderate ( $L_{A01}$ : $r\approx 0.5$ ) to moderately strong ( $L_{A05}$ : $r\approx 0.7$ ) and then to very strong ( $L_{A10}$ : $r\approx 0.8$ ) in both time intervals. Regarding the maximum noise indicator, a moderate correlation was obtained ( $L_{Amax}$ : $r\approx 0.5$ ). Opposite to equivalent-based relationships, by increasing the time interval (from 1-h to 8-h), the dispersion of data ( $R^2$ metric) was slightly increased. This results in the slight increase in the correlation coefficient of the maximum and percentile noise indicator-based relationships.

Finally, cumulative probability distributions (CPDs) were analyzed to provide a comprehensive understanding of how outdoor-to-indoor noise attenuation varies, revealing distributional patterns, across outdoor noise level groups, noise indicators, temporal intervals, and background noise conditions. Specifically, CPDs of level differences were computed for grouped outdoor exposure levels (40, 50, 60, 70, 80, and 90 dB(A)), using increments of ± 5 dB(A). Because data availability differed across groups, some distributions reflect only the subsets with sufficient sample size. Figure 4 presents the resulting CPDs. For 1-h intervals, the $L_{Aeq}$ -based CPDs exhibit greater spread than those for 8-h interval. When comparing the CPDs across the two indoor background noise conditions, the 6 dB(A) condition exhibits tighter (less variable) distributions than the 10 dB(A) condition, primarily due to the larger number of available noise levels under the former condition. Across the remaining indicators, the influence of outdoor-level grouping is clearly visible in both time-interval steps. The CPDs of $L_{Amax}$ and $L_{A01}$ show that higher outdoor levels lead to reduced level differences and wider distributional spread, consistent with the dominance of high-intensity noise events. In comparison, the CPDs of $L_{A05}$ and $L_{A10}$ exhibit relatively narrower distributions, reflecting their lower sensitivity to extreme events.

Figure 4.

Cumulative probability distribution (CPD) of outdoor-to-indoor level differences grouped by outdoor exposure levels: 40 dB(A), 50 dB(A), 60 dB(A), 70 dB(A), 80 dB(A), and 90 dB(A), using increments of ± 5 dB(A). The rows represent: (top) $L_{Aeq}$ levels with BGN conditions of 6 and 10 dB(A) across 1 and 8 h time intervals; (mid) $L_{Amax}$ and $L_{A01}$ levels across 1 and 8 h time intervals; and (bottom) $L_{A05}$ and $L_{A10}$ across 1 and 8 h time intervals.

Multiple linear regression modeling

The summaries of the multiple linear regression models are presented in Table 2. As shown, increasing the time interval from 1 to 8 h led to higher explanatory power ( $R^2$ ) across all noise indicators. Focusing on the $L_{Aeq}$ models, the two indoor background noise conditions yielded different model fits. For the 1-h period, $R^2=0.58$ (BGN: 6 dB(A)) and $R^2=0.86$ (BGN: 10 dB(A)); for the 8-h period, $R^2=0.76$ (BGN: 6 dB(A)) and $R^2=0.90$ (BGN: 10 dB(A)). Similar trends were observed for the maximum ( $R^2=0.41$ for 1 h, $R^2=0.68$ for 8 h), and percentile-based models ( $R^2\approx 0.60$ for 1 h and $R^2\approx 0.70$ for 8 h).

Table 2.

Estimation of the parameters for multiple linear regression models, including the modeling performance (RMSE).

$\Delta L_{Aeq,1h,06dB,Out-In}$

$\Delta L_{Aeq,1h,10dB,Out-In}$

$\Delta L_{Aeq,8h,06dB,Out-In}$

$\Delta L_{Aeq,8h,10dB,Out-In}$

Predictor

Symbol †

Coef.

95% CI

p-Value

Coef.

95% CI

p-Value

Coef.

95% CI

p-Value

Coef.

95% CI

p-Value

(Intercept)

${\beta }_0$

24.27

[23.77, 24.78]

<0.001

21.01

[20.42, 21.60]

<0.001

22.74

[22.03, 23.45]

<0.001

22.80

[22.14, 23.47]

<0.001

$L_{Aeq,Out}$

${\beta }_1$

0.57

[0.51, 0.64]

<0.001

0.85

[0.78, 0.92]

<0.001

0.48

[0.39, 0.57]

<0.001

1.03

[0.91, 1.15]

<0.001

Site type

ST = [1]

0

0

0

0

Site type

ST = [2]

−3.05

[−4.13,−1.97]

<0.001

1.80

[0.34,3.27]

0.016

−1.38

[−2.52,−0.23]

0.019

1.70

[0.03, 3.37]

<0.001

Window size

${\beta }_2$

−0.50

[−0.87, −0.13]

0.008

−2.05

[−2.86,−1.24]

<0.001

−8.04

[−9.27, −6.81]

<0.001

Window type

WT = [1]

0

Window type

WT = [2]

2.86

[1.43,4.38]

<0.001

Occupation status

OS = [1]

0

0

0

0

Occupation status

OS = [2]

1.96

[0.98, 2.94]

<0.001

2.30

[1.42, 3.17]

<0.001

7.01

[5.81, 8.20]

<0.001

4.94

[3.62, 6.27]

<0.001

Room volume

${\beta }_3$

−0.09

[−0.12, −0.05]

<0.001

$n$ / β error

371/0.008

149/0.020

94/0.025

50/0.054

$R^2$ / $R_{adj}^2$

0.583/0.577

0.858/0.855

0.762/0.751

0.903/0.894

RMSE (dB(A))

4.30

2.70

2.50

2.30

$\Delta L_{Amax,1h,Out-In}$

$\Delta L_{Amax,8h,Out-In}$

$\Delta L_{A01,1h,Out-In}$

$\Delta L_{A01,8h,Out-In}$

Predictor

Symbol †

Coef.

95% CI

p-Value

Coef.

95% CI

p-Value

Coef.

95% CI

p-Value

Coef.

95% CI

p-Value

(Intercept)

${\beta }_0$

22.67

[22.10, 23.24]

<0.001

18.15

[17.31, 18.98]

<0.001

22.87

[22.46, 23.29]

<0.001

24.31

[23.67, 24.97]

<0.001

$L_{Ai,Out}$

${\beta }_1$

0.42

[0.38, 0.46]

<0.001

0.70

[0.59, 0.80]

<0.001

0.30

[0.27, 0.33]

<0.001

0.43

[0.35, 0.51]

<0.001

Site type

ST = [1]

0

0

0

0

Site type

ST = [2]

−2.50

[−3.33, −1.68]

<0.001

−1.72

[−3.38, 0.07]

0.040

−2.85

[−3.45, −2.25]

<0.001

−1.42

[−2.69, −0.15]

0.029

Window size

${\beta }_2$

−0.20

[−0.37, −0.03]

0.025

Window type

WT = [1]

0

0

Window type

WT = [2]

2.25

[1.20, 3.29]

<0.001

3.77

[3.00, 4.54]

<0.001

Occupation status

OS = [1]

0

0

0

0

Occupation status

OS = [2]

4.21

[3.36, 5.06]

<0.001

8.20

[6.51, 9.88]

<0.001

5.72

[5.11, 6.34]

<0.001

5.40

[4.09, 6.71]

<0.001

$n$ / ${\beta }_{error}$

869/0.001

130/0.023

820/0.001

133/0.022

$R^2$ / $R_{adj}^2$

0.412/0.409

0.681/0.673

0.555/0.553

0.579/0.569

RMSE (dB(A))

5.70

4.70

4.00

3.60

$\Delta L_{A05,1h,Out-In}$

$\Delta L_{A05,8h,Out-In}$

$\Delta L_{A10,1h,Out-In}$

$\Delta L_{A10,8h,Out-In}$

Predictor

Symbol †

Coef.

95% CI

p-Value

Coef.

95% CI

p-Value

Coef.

95% CI

p-Value

Coef.

95% CI

p-Value

(Intercept)

${\beta }_0$

23.13

[22.73, 23.52]

<0.001

23.62

[22.92, 24.33]

<0.001

23.11

[22.73, 23.48]

<0.001

24.73

[24.09, 25.37]

<0.001

$L_{Ai,Out}$

${\beta }_1$

0.40

[0.37, 0.42]

<0.001

0.55

[0.47, 0.62]

<0.001

0.49

[0.45, 0.51]

<0.001

0.63

[0.56, 0.70]

<0.001

Site type

ST = [1]

0

0

0

0

Site type

ST = [2]

−2.51

[−3.06, −1.95]

<0.001

−2.00

[−3.09, −0.90]

<0.001

−2.05

[−2.58, −1.51]

<0.001

−1.21

[−2.51, −0.27]

<0.001

Window type

WT = [1]

0

0

0

0

Window type

WT = [2]

2.89

[2.16, 3.62]

<0.001

3.11

[1.70, 4.52]

<0.001

2.47

[1.77, 3.17]

<0.001

1.52

[0.28, 2.75]

<0.001

Occupation status

OS = [1]

0

0

0

0

Occupation status

OS = [2]

4.18

[3.60, 4.76]

<0.001

4.26

[3.100, 5.42]

<0.001

3.27

[2.72, 3.83]

<0.001

2.06

[1.02, 3.11]

<0.001

$n$ / ${\beta }_{error}$

835/0.001

137/0.022

848/0.001

131/0.023

$R^2$ / $R_{adj}^2$

0.605/0.603

0.691/0.681

0.649/0.648

0.750/0.742

RMSE (dB(A))

3.80

3.10

3.70

2.60

†

Symbols in equations (1)–(12).

i : max, 01, 05, and 10.

ST: [1]: Road-Traffic Exposure and [2]: Multi Exposure. WT: [1]: Single-Layered and [2]: Multi-Layered. OS: [1]: Occupied and [2]: Unoccupied.

[1]: Reference level.

All multiple linear regression models showed a statistically significant positive association between outdoor noise exposure and the outdoor-to-indoor level difference ( $\Delta L_{Ai}$ ). For $L_{Aeq}$ models, a 1 dB(A) increase in outdoor levels resulted in $\Delta L_{Aeq}$ increase of 0.57 dB(A) in the 1-h model and 0.48 dB(A) in the 8-h model, both based on the 6 dB(A) background noise condition. When using the stricter 10 dB(A) condition, the effect estimates increased to 0.85 and 1.03 dB(A) for the 1-h and 8-h models, respectively. This suggests that applying a higher background noise condition reduces variability in indoor noise levels due to indoor sources and improves the signal-to-noise ratio in the models. The influence of temporal resolution was consistent across all noise metrics, showing stronger associations at the 8-h resolution. For $L_{Amax}$ , a 1 dB(A) increase in outdoor noise level led to an increase in $\Delta L_{Amax}$ of 0.42 dB(A) for the 1-h model and 0.70 dB(A) for the 8-h model. Percentile-based indicators ( $\Delta L_{AN}$ ) followed similar trends, with a 1 dB(A) increase in outdoor noise level led to increases ranging from 0.30 to 0.63 dB(A). These findings underscore the importance of both temporal aggregation and indoor background noise conditions in shaping the estimated relationships between outdoor noise exposure levels and outdoor-to-indoor level differences. Longer averaging periods likely smooth noise exposure variability, while stricter conditions improve data quality by excluding measurements influenced by the indoor background noise levels.

The proportion of the explained variance by each predictor in the multiple linear regression models was calculated and the results are presented in Figure 5. As it can be seen, the outdoor noise levels explained the greater percentage of variance across all the models ( $L_{Aeq,Out}:$ 36%–53%, $L_{Amax,Out}$ : 31%–41%, and $L_{AN,Out}$ : 26%–67%). The window size, the site type, and the occupation status predictors explained most of the additional variability in the equivalent noise indicator models. Regarding the maximum and the first percentile noise indicator models, the occupation status predictor explained most of the additional variability. In the fifth and the 10th percentile noise indicator models, the window type and the occupation status predictors explained most of the additional variability.

Figure 5.

Relative importance for each predictor in multiple linear regression models.

Finally, the multiple linear regression models were validated using 10-fold cross-validation procedure, and the main diagnostic results are presented in Table 2. In addition to this, a comparison between the predicted and observed outdoor-to-indoor level differences for each noise indicator, along with corresponding diagnostics, is shown in Figure 6. Focusing on Figure 6, the models based on the equivalent noise indicator with the 10 dB(A) background noise condition exhibited lower RMSE levels (1-h: RMSE = 2.7 dB(A) and 8-h: RMSE = 2.3 dB(A)) compared to those based on the 6 dB(A) background noise condition (1-h: RMSE = 4.3 dB(A) and 8-h: RMSE = 2.5 dB(A)). When comparing the RMSE levels of the maximum and percentile indicator models, it was evident that the $L_{Amax}$ models extracted the largest RMSE levels (1-h: RMSE = 5.7 dB(A) and 8-h: RMSE = 4.7 dB(A)). In contrast, the $L_{A10}$ models exhibited the lowest RMSE levels (1-h: RMSE = 3.7 dB(A) and 8-h: RMSE = 2.6 dB(A)). The $L_{A01}$ (1-h: RMSE ≈ 4.0 dB(A) and 8-h: RMSE 3.6 dB(A)) and $L_{A05}$ (1-h: RMSE ≈ 3.8 dB(A) and 8-h: RMSE ≈ 3.1 dB(A)) models presented greater RMSE levels compared with the $L_{A10}$ models.

Figure 6.

Validation of multiple linear regression models via the 10-fold cross-validation procedure, plotting the observed levels (Obs.) versus the estimated levels (Est.) with respect to (top) $L_{Aeq}$ , (mid-left) $L_{Amax}$ , (mid-right) $L_{A01}$ , (bottom-left) $L_{A05}$ , and (bottom-right) $L_{A10}$ noise indicators, including their diagnostics.

Mixed-effect linear regression modeling

The summaries of mixed-effect linear regression models were extracted and are presented in Table 3. As it is seen from Table 3, the predictors vary among the $L_{Aeq}$ models. The two background noise levels yielded different levels of explanatory power for 1-h ( $L_{Aeq,6dB}$ : $R_M^2$  = 0.27 and $L_{Aeq,10dB}$ : $R_M^2$  = 0.31) and 8-h ( $L_{Aeq,6dB}$ : $R_M^2$  = 0.40 and $L_{Aeq,10dB}$ : $R_M^2$  = 0.72) interval. Focusing on the $L_{Amax}$ models, analogous explanatory power was found for 1-h ( $R_M^2$  = 0.38) and 8-h ( $R_M^2$  = 0.49) time periods. Regarding the $L_{AN}$ models, a clear increase to $R_M^2$ was obtained after increasing the time interval from 1-h to 8-h.

Table 3.

Estimation of the parameters for mixed-effect linear regression models, including the modeling performance (RMSE).

		$\Delta L_{Aeq,1h,06dB,Out-In}$			$\Delta L_{Aeq,8h,06dB,Out-In}$			$\Delta L_{Aeq,1h,10dB,Out-In}$			$\Delta L_{Aeq,8h,10dB,Out-In}$
Predictor	Symbol †	Coef.	95% CI	p-Value	Coef.	95% CI	p-Value	Coef.	95% CI	p-Value	Coef.	95% CI	p-Value
(Intercept)	${\beta }_0$	21.78	[18.90, 24.67]	<0.001	24.51	[22.55, 24.45]	<0.001	23.51	[20.82, 26.20]	<0.001	23.52	[21.79, 25.52]	<0.001
$L_{Aeq,Out}$	${\beta }_1$	0.31	[0.27, 0.35]	<0.001	0.58	[0.44, 0.71]	<0.001	0.19	[0.14, 0.25]	<0.001	0.92	[0.78, 1.06]	<0.001
Window size	${\beta }_2$										−8.63	[−8.63, −4.12]	<0.001
Occupation status	OS = [1]	0
Occupation status	OS = [2]	3.89	[1.79, 7.39]	0.039
Room volume	${\beta }_3$				−0.19	[−0.33, −0.04]	0.020	−0.23	[−0.44, −0.02]	0.048
$n$ / $R_M^2$		340/0.267			80/0.397			124/0.309			40/0.727
RMSE (dB(A))		1.30			0.90			0.7			0.8
		$\Delta L_{Amax,1h,Out-In}$			$\Delta L_{Amax,8h,Out-In}$			$\Delta L_{A01,1h,Out-In}$			$\Delta L_{A01,8h,Out-In}$
Predictor	Symbol †	Coef.	95% CI	p-Value	Coef.	95% CI	p-Value	Coef.	95% CI	p-Value	Coef.	95% CI	p-Value
(Intercept)	${\beta }_0$	20.92	[18.66, 23.17]	<0.001	14.16	[11.05, 17.26]	<0.001	22.14	[19.59, 24.68]	<0.001	25.74	[23.71, 27.77]	<0.001
$L_{Ai,Out}$	${\beta }_1$	0.45	[0.41, 0.49]	<0.001	0.66	[0.53, 0.79]	<0.001	0.31	[0.29, 0.33]	<0.001	0.57	[0.49, 0.65]	<0.001
Occupation status	OS = [1]	0			0			0
Occupation status	OS = [2]	4.23	[1.24, 7.23]	<0.001	8.52	[4.74, 12.30]	<0.001	3.65	[0.26, 7.04]	<0.001
$n$ / $R_M^2$		844/0.379			134/0.489			849/0.239			112/0.346
RMSE (dB(A))		3.60			4.90			2.10			1.10
		$\Delta L_{A05,1h,Out-In}$			$\Delta L_{A05,8h,Out-In}$			$\Delta L_{A10,1h,Out-In}$			$\Delta L_{A10,8h,Out-In}$
Predictor	Symbol †	Coef.	95% CI	p-Value	Coef.	95% CI	p-Value	Coef.	95% CI	p-Value	Coef.	95% CI	p-Value
(Intercept)	${\beta }_0$	21.65	[19.24, 24.06]	<0.001	26.05	[24.48, 27.64]	<0.001	21.82	[19.59, 24.04]	<0.001	25.98	[24.58, 27.38]	<0.001
$L_{Ai,Out}$	${\beta }_1$	0.28	[0.27, 0.30]	<0.001	0.36	[0.27, 0.45]	<0.001	0.33	[0.31, 0.35]	<0.001	0.55	[0.40, 0.61]	<0.001
Occupation status	OS = [1]	0						0
Occupation status	OS = [2]	3.50	[0.30, 6.71]	<0.001				3.24	[0.27, 6.20]	<0.001
$n$ / $R_M^2$		760/0.243	129/0.234	822/0.305	132/0.420
RMSE (dB(A))		1.40	1.30	1.40	1.40

†

Symbols in equations (13)–(24).

$i$ : max, 01, 05, and 10.

OS: [1]: Occupied, and [2]: Unoccupied.

[1]: Reference level.

Across all mixed-effect linear regression models, a consistent positive association was observed between outdoor noise levels and the outdoor-to-indoor level difference ( $\Delta L_{Ai}$ ), with effect estimates generally increasing with coarser temporal resolution. For the $L_{\mathrm{Aeq}}$ models, a 1 dB(A) increase in $L_{\mathrm{Aeq},\mathrm{Out}}$ was associated with an increase in $\Delta L_{\mathrm{Aeq}}$ of 0.31 dB(A) in the 1-h model and 0.58 dB(A) in the 8-h model under the 6 dB(A) indoor background noise condition. When applying the stricter 10 dB(A) condition, the corresponding estimates increased from 0.19 dB(A) (1-h) to 0.92 dB(A) (8-h). For the $L_{\mathrm{Amax}}$ models, a 1 dB(A) increase in $L_{\mathrm{Amax},Out}$ resulted in increases in $\Delta L_{\mathrm{Amax}}$ of 0.45 dB(A) (1-h) and 0.66 dB(A) (8-h). Similar trends were observed in percentile indicators. These results highlight that both the choice of temporal resolution and background noise condition substantially influence the strength and stability of the observed associations. Coarser temporal aggregation reduces the impact of short-term fluctuations, while stricter background noise criterion appears to reduce measurement variability and enhance explanatory power.

The percentage of explained variance by each predictor ( $R_M^2$ ) was assessed for all the models and the results are presented in Figure 7. As seen, the outdoor levels explained the greater percentage of variance across all the models ( $L_{\mathrm{Aeq}}:$ 13%–31%, $L_{Amax}$ : 23%–24%, $L_{AN}$ : 12%–22%). The occupation status, window size, and room volume predictors as well as the intercept explained most of the additional variability in the various equivalent models. Regarding the maximum and the percentile indicator models, the occupation status predictor explained most of the additional variability.

Figure 7.

Relative importance for each predictor in mixed-effect linear regression models. Note that in the multiple linear models, the intercept is excluded from the relative importance analysis, as it does not contribute to the explained variance in the estimation of outdoor-to-indoor level differences. In contrast, the mixed-effect models include a random intercept (location ID), which captures location-level variance and is thus reflected in the proportion of explained variance.

Similar to the multiple linear regression models, the mixed-effect linear regression models were validated with respect to the 10-fold cross-validation procedure and the main diagnostic (RMSE) is included into Table 3. A comparison between the predicted and observed outdoor-to-indoor level differences for each noise indicator, along with corresponding diagnostics, is shown in Figure 8. Focusing on Figure 8, the equivalent noise indicator models with the 10 dB(A) background noise condition exhibited lower RMSE levels (1-h: RMSE = 0.7 dB(A) and 8-h: RMSE = 0.8 dB(A)) compared with those based on the 6 dB(A) background noise condition (1-h: RMSE = 1.3 dB(A) and 8-h: RMSE = 0.9 dB(A)). When comparing the RMSE levels of the maximum and percentile indicator models, it was evident that the $L_{Amax}$ models had the largest RMSE levels (1-h: RMSE = 3.6 dB(A) and 8-h: RMSE = 4.9 dB(A)). The percentile models exhibited RMSE levels between 1.1 and 2.1 dB(A) in both time intervals.

Figure 8.

Validation of mixed-effect linear regression models via the 10-fold cross-validation procedure, plotting the observed levels (Obs.) versus the estimated levels (Est.) with respect to (top) $L_{Aeq}$ , (mid-left) $L_{Amax}$ , (mid-right) $L_{A01}$ , (bottom-left) $L_{A05}$ , and (bottom-right) $L_{A10}$ noise indicators, including their diagnostics.

Finally, the lower root mean square error (RMSE) values obtained from the mixed-effect linear models, in comparison to the multiple linear regression models, suggest that the inclusion of random intercept effect enhances model performance and provides a more accurate representation of the estimated outdoor-to-indoor level differences.

Single-valued attenuation level factors

Using both modeling approaches, the mean and standard deviation of the estimated outdoor-to-indoor attenuation levels were determined as a function of the noise indicator, the background noise condition, and the time interval. Consequently, indoor noise levels can be derived from outdoor measurements by applying a single-valued outdoor-to-indoor attenuation factor. These attenuation factors are reported in Figure 9 (left), together with the absolute differences between the estimated and measured (observed) levels. Overall, the estimated attenuation factors showed only minor differences between the multiple linear regression models (MLRMs) and the mixed-effect linear regression models (MELRMs). Finally, the analysis of absolute differences between estimated and observed single-valued levels for each noise indicator in Figure 9, (right) shows patterns consistent with those in Figures 6 and 8. Both modeling approaches yield absolute mean level differences below 3 dB(A) for all indicators except the maximum noise indicator. Mixed-effects linear regression models achieve up to 2 dB(A) lower absolute mean differences than multiple linear regression models, indicating better performance. In contrast, the maximum noise indicator exhibited an absolute mean difference of approximately 3 dB(A), marking the only significant deviation from the overall trend and underscoring the difficulty in accurately obtaining predictions for this metric.

Figure 9.

Mean and standard deviation (error-bars) of estimated attenuation level factors (left) per noise indicator and setting, accounting for background noise conditions (6 and 10 dB(A)) and time intervals (1 and 8 h), based on multiple (MLRMs) and mixed-effect linear regression models (MELRMs). Heatmap (right) denotes the absolute level difference $\left|\Delta L_{A,i}-\Delta {\widehat{L}}_{A,i}\right|$ between the observed $\Delta L_{A,i}$ and estimated $\Delta {\widehat{L}}_{A,i}$ mean level difference per noise indicator $i$ .

Discussion

To produce estimates of indoor noise exposure at night, outdoor, and indoor noise measurements from 49 dwellings in London were used to derive attenuation levels for various noise indicators with respect to two time intervals of 1-h and 8-h. The influence of indoor background noise was accounted for in the $L_{Aeq}$ levels by applying two threshold criteria (6 and 10 dB(A)). Following data cleaning and minimization of the (indoor) background noise levels, moderate-to-strong correlations between outdoor levels and outdoor-to-indoor level differences for 1-h and 8-h averaging periods were obtained. Therefore, regression modeling techniques were applied to predict the outdoor-to-indoor attenuation levels based on known factors relating to the outdoor and indoor environment as well as building façade characteristics for explaining the percentage of unexplained variance in the estimated quantity. In particular, multiple linear regression models permit the estimation of the outdoor-to-indoor level difference in a more “generalized” manner compared to mixed-effect linear regression models that consider information related to the location ID, accounting for repeated measures of noise exposure per dwelling. Across most noise indicators, mixed-effect models outperformed multiple linear models, achieving lower RMSE values (0.7–4.9 dB(A) vs 2.3–5.7 dB(A)). The adoption of the stricter background noise threshold further enhanced model performance by reducing the influence of indoor background noise. Among the predictors, outdoor sound levels accounted for the greatest share of variability, complemented by effects from occupation status, window size, room volume, and location ID. Estimated indoor sound attenuation spanned 20–26 dB(A) depending on the noise indicator.

Assessment of outdoor levels and outdoor-to-indoor level differences

Typically, short-term measurements and a short integration time (e.g. 1 s) are used to assess outdoor-to-indoor noise exposure level differences, following a supervised (controlled) approach. Locher et al. ²⁰ conducted outdoor and indoor measurements for 3 min using an integration time of one second and employing a supervised approach. In this way, the contribution of indoor noise sources was minimized. Pirrera et al. ⁴⁵ evaluated outdoor and indoor noise exposure for seven consecutive days and 7 h (23:00–07:00) using an integration time of 30 s and an unsupervised approach. Short integration time (e.g. 1 s) results in a higher resolution of noise exposure and its events during the considered time-interval period. In our study, the employed 1-min integration time results in a moderate resolution of noise exposure during the time-interval periods.

At night-time the background noise level indoors is lower than at day-time. This suggests that the quantification of indoor night-time noise exposure based on the outdoor noise exposure is likely to provide a less biased estimate of the “true” exposure due to the low degree of background noise. To ensure that only the transmitted noise from the external to the internal environment was assessed (due to unsupervised approach), indoor noise levels should not dominate the outdoor noise exposure levels. Moreover, in occupied conditions, people tend to generate noise, ⁴⁶ acting as secondary sound sources, especially before and after sleeping, ⁴⁷ resulting in higher indoor noise levels compared to indoor levels caused by outdoor noise sources. Our study was conducted with an average of 1–3 occupants per dwelling. This indicates that the background noise levels may have a significant impact on the noise levels recorded in the indoor environment. By quantifying indoor background noise levels via the percentile noise indicator $L_{A99}$ and defining two criteria (6 and 10 dB(A)), the impact of the background noise on the equivalent outdoor-to-indoor noise levels was alleviated. The latter was also verified by the spectral characteristics of the outdoor-to-indoor levels. ⁴⁸ Note that this represents an important step in the process of employing unsupervised measurement methodologies in order to explore representative outdoor-to-indoor level differences with respect to noise indicators, where the outdoor-based indoor levels were obtained via a non-supervised approach.

In captured outdoor noise exposure levels, various correction factors corresponding to the position of outdoor microphones have been applied (e.g. Locher et al., ²⁰ Müller-Trapet, ⁴⁹ and Ryan et al. ⁵⁰ ). These correction factors reduce the impact of destructive and constructive wave interferences (mainly at low frequencies) that occur due to the distance between the outdoor noise receivers and the building façade across different frequency bands.^51,52 In our study, we did not use any correction factor for the outdoor noise levels due to the lack of information related to the exact position of outdoor equipment from façade structures. This may result in a systematic error in outdoor measurements; and therefore, in outdoor-to-indoor level differences.

Focusing on the explored relationships between the outdoor noise exposure levels and the outdoor-to-indoor noise exposure level differences, a positive gradient is presented. Similar gradients have been also reported with respect to time-eq25 levels ²⁰ and spectral time-equivalent levels. ⁴⁸ This is associated to the variations in the façade characteristics and background noise levels as well as to the positions and the characteristics of various sound sources with respect to the positions of both outdoor and indoor microphones in the locations. Furthermore, the sound insulation is usually better at locations where there is more environmental noise. ⁵³ This denotes the importance of further research on the explored relationships with respect to the design criteria. A recent study, ²⁹ based on the same dataset, investigated the relationship between A-weighted equivalent outdoor-to-indoor level differences and outdoor noise levels across daytime, evening, and night-time periods, highlighting a significant influence of the time period on these relationships and indicating the importance of time-period in the assessment and estimation of attenuation levels.

In terms of noise indicators and the obtained cumulative probability distributions, the $L_{Aeq}$ -based CPDs for the 6 dB(A) indoor background noise condition showed less variability than those for the 10 dB(A) condition, which is attributable to the larger number of available outdoor noise levels under the former. For the 1-h intervals, the increased spread in the CPDs reflects the higher variability in façade insulation performance and its contributing components. CPDs of $L_{Amax}$ and $L_{A01}$ show lower attenuation and broader distributions at higher exposures, reflecting sensitivity to high-intensity noise events. Furthermore, CPDs of $L_{A05}$ present intermediate behavior, while CPDs of $L_{A10}$ remains stable across groups. The finding related to the $L_{Amax}$ , $L_{A01}$ , and $L_{A10}$ are aligned with previous findings indicating that $L_{Amax}$ exhibits greater variability in exposure levels compared to $L_{A01}$ , ⁵⁴  while $L_{A10}$ serves as a more “robust” metric for noise exposure assessment, reducing the variability in strong event-based exposure levels.

According to the World Health Organisation (WHO), ⁵⁵ the average outdoor-to-indoor level differences for closed windows is usually estimated around 25 dB(A). However, in literature,^20,29,45,56 attenuation factors up to 32 dB(A) are presented. In our study, similar results to those presented by the WHO were found for the equivalent noise indicator, with the highest deviation from the WHO level being approximately 3 dB(A). The position of the equipment, the façade properties (e.g. classification) and its components (e.g. wall and window mounting characteristics) in relation to the position of sound sources (angle of incidence), as well as the type of noise source, are responsible for deviations in attenuation factors. Therefore, it is important to use the values for attenuation with caution in studies with different site, building, and exposure characteristics. This is of particular importance, when the relationship between noise exposure and health outcomes is to be investigated. These underscore the necessity of harmonized measurement protocols that are aligned with the specific objectives of the assessment (e.g. sound insulation performance, sleep disturbance, or cognitive outcomes), thereby facilitating more robust and comparable results across different studies.

Finally, indoor noise exposure levels derived from outdoor measurements by applying a single-valued outdoor-to-indoor attenuation factor are likely to provide a less biased estimate of the “true” outdoor-based indoor exposure levels than only using outdoor levels as proxy for indoor levels. However, this approach is centered to outdoor-based indoor noise exposure, thereby excluding the contribution of indoor sound sources to the overall indoor noise exposure. Hence, this approach may be of particular interest to exposure scientists and epidemiologists seeking to estimate indoor noise levels from outdoor estimates during nighttime.

Regression modeling

Both multiple and mixed-effect linear regression models were developed for estimating outdoor-to-indoor level differences. Overall, mixed-effect linear regression models presented lower RMSE levels in comparison with multiple linear regression models. The highest RMSE levels were observed in the maximum noise indicator ( $L_{Amax}$ ) models, suggesting that the source position and façade factors may be responsible for the unexplained variability in residuals. However, information related to the façade was not recorded. In order to gain a deeper understanding of the performance of the regression models, it is necessary to consider the RMSE levels in relation to the ability of a healthy ear to perceive a change in noise level (perceptible level difference). ⁵⁷ Specifically, a 3 and a 5 dB(A) RMSE level is associated to a just perceptible and a clearly perceptible level difference, respectively. ⁵⁷ In multiple linear regression models, the RMSE levels across all indicators lied between the 3 and 5 dB(A), indicating that the estimated outdoor-to-indoor noise levels are into the range of just and clear perceptible level difference. However, in mixed-effect linear regression models, the RMSE levels were well below the 3 dB(A), except for the maximum noise indicator models, indicating a non-audible level difference between the estimated and the observed outdoor-to-indoor level difference. For the longer time interval (8-h), a lower degree of systematic error is mostly anticipated in the estimation of façade attenuation based on the equivalent, maximum, and percentile indicators. Similarly, there will be a lower degree of a systematic error in the estimation of equivalent levels based on the 10 dB(A) background noise condition compared with the levels based on the 6 dB(A) background noise condition. Finally, for further verifying these modeling approaches, extensive noise-exposure measurements, complemented by data on sound insulation and room acoustics, need to be considered.

Application

A methodology for estimating night-time (23:00–07:00) outdoor-to-indoor level differences based on unsupervised and (time) synchronized outdoor and indoor measurements was proposed. Based on this procedure, outdoor and indoor noise levels influenced by dominant indoor (secondary) noise sources and indoor background noise levels were minimized, especially in the case of the equivalent noise levels, where two background noise conditions were applied. The validation of this procedure based on both the time-averaged (presented in this study) and spectral-averaged (see Terzakis et al. ⁴⁸ ) analyses strengthens the latter statements. The analyses based on two different background noise conditions in equivalent levels present mean differences of 1 and 2 dB(A), respectively. Finally, the analyses based on two different time intervals suggest the importance of specifying the resolution when attenuation levels need to be applied. In our case, mean differences of up to 1.5 dB(A) were obtained between the two time intervals across the equivalent and percentile noise indicators, while for the maximum level the change reached up to 4 dB(A).

Although single-valued outdoor-to-indoor attenuation factors can be used for the estimation of indoor levels based on the outdoor ones, prediction models are capable to provide more reliable attenuation factors, relying on the different building, outdoor, and indoor characteristics. The developed models are applicable to data with similar noise exposure levels and building characteristics in the United Kingdom due to the fact that all the measurements used were conducted in the Greater London area. It should, however, be noted that building façade characteristics may vary significantly in other areas. Hence, the models, and especially the mixed-effect linear regression models, should be used with caution in locations with different building characteristics. Finally, the approach for capturing the noise exposure levels should be comply with the presented methodology, since outdoor-to-indoor level differences will significantly vary.

Conclusions

In this study, a methodology to derive night-time outdoor-to-indoor attenuation levels was developed, by incorporating unsupervised and synchronized outdoor and indoor noise exposure measurements and information on building characteristics in regression modeling. The method minimized the presence of dominant indoor noise sources and background noise levels. The produced attenuation factors are from UK data reflecting local noise sources and building characteristics. The methods may be used in other countries but would benefit verification with local data/conditions. The proposed methods and resulting attenuation factors for various indicators beyond $L_{Aeq}$ may be of interest to exposure scientists and epidemiologists seeking to estimate indoor noise levels from estimate outdoor levels at nighttime.

Enhancing the reliability of outdoor-to-indoor noise characterization requires a broader dataset with more measurements per location ID, particularly for the equivalent noise indicator and under non-supervised conditions. Incorporating additional predictors describing detailed building façade structure characteristics would improve the estimation of noise transmission pathways and account for structural variability across buildings. Therefore, for future research, extensive noise exposure measurements, complemented by data on sound insulation and room acoustics, could be conducted across diverse locations and countries. Such efforts are could refine and validate the models and enable more accurate estimation of indoor noise levels from outdoor exposures and outdoor-to-indoor level differences.