Archives of Acoustics, 45, 4, pp. 613–623, 2020

Determining the Number of Measurements and Bootstrap Samples Required to Estimate of Long-Term Noise Indicators

Bartłomiej STĘPIEŃ
AGH University of Science and Technology

The minimum size of the bootstrap algorithm input parameters have been determined for estimation of long-term indicators of road traffic noise. Two independent simulation experiments have been performed for that purpose. The first experiment served to determine the impact of original random sample size, and the second to determine the impact of number of the bootstrap replications on the accuracy and uncertainty of estimation of long-term noise indicators. The inference has been carried out based on results of non-parametric statistical test at significance level α = 0.05. The simulation experiments have shown that estimation of long-term noise indicators with uncertainty below ±1 dB(A) requires all-day noise measurements during three randomly selected days during the year in a dense urban development. The maximum size of original random sample should not exceed n = 50 elements. The minimum number of bootstrap replications necessary for estimation should be B = 5000. The data used to the simulation experiments and carry out the analysis were results of continuous monitoring of road traffic noise recorded in 2009 in one of the main arteries of Krakow in Poland.
Keywords: bootstrap; bootstrap replications; long-term noise indicators; number of measurements; uncertainty; accuracy
Full Text: PDF
Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).


Batko W., Pawlik P. (2012), Uncertainty evaluation in modelling of acoustic phenomena with uncertain parameters using interval arithmetic, Acta Physica Polonica A, 121(1–A): A-152–A-155,, doi: 10.12693/APhysPolA.121.A-152.

Batko W., Pawlik P. (2013), New method of uncertainty evaluation of the sound insulation of partitions, Acta Physica Polonica A, 123(6): 1012–1015, doi: 10.12693/APhysPolA.123.1012.

Batko W., Stępień B. (2010), Application of the bootstrap estimator for uncertainty analysis of the long-term noise indicators, Acta Physica Polonica A, 118(1): 11–16, doi: 10.12693/APhysPolA.118.11.

Brambilla G., Castro F.L., Cerniglia A., Verardi P. (2007), Accuracy of temporal samplings of environmental noise to estimate the long-term Lden value, [in:] 36th International Congress and Exhibition on Noise Control Engineering INTER-NOISE 2007, Turkish Acoustical Society, Istanbul, Turkey, pp. 4082-4089.

Brambilla G., Gallo V., Zambon G. (2015), Prediction of accuracy of temporal sampling applied to non-urban road traffic noise,Journal of Pollution Effects and Control, 3(3): 147, doi: 10.4172/2375-4397.1000147.

Don C.G., Rees I.G. (1985), Road traffic sound level distributions, Journal of Sound and Vibration, 100(1): 41–53, doi: 10.1016/0022-460X(85)90341-4.

Efron B. (1979), Bootstrap methods: another look at the jackknife, Annals of Statistics, 7(1): 1–26.

Efron B., Tibshirani R.J. (1993), An introduction to the bootstrap, Chapman & Hall/CRC, New York.

European Parliament (2002), Directive 2002/49/EC of the European Parliament and of the Council of 25 June 2002 relating to the assessment and management of environmental noise.

Farrelly F.A., Brambilla G. (2003), Determination of uncertainty in environmental noise mesurements by bootstrap method, Journal of Sound and Vibration, 268(1): 167–175, doi: 10.1016/S0022-460X(03)00195-0.

Gaja E., Giménez A., Sancho S., Reig A. (2003), Sampling techniques for the estimation of the annual equivalent noise level under urban traffic conditions , Applied Acoustics, 64(1): 43–53, doi: 10.1016/S0003-682X(02)00050-6.

Giménez A., González M. (2009), A stochastic model for the noise levels, Journal of the Acoustical Society of America, 125(5): 3030–3037, doi: 10.1121/1.3109980.

Heiss A., Krapf K.G. (2007), Quantification of uncertainty by real time confidence limits in separation of sound immission levels, Noise Control Engineering Journal, 55(1): 149–158, doi: 10.3397/1.2710947.

Huang N., Elhilali M. (2017), Auditory salience using natural soundscapes, Journal of the Acoustical Society of America, 141(3): 2163–2176, doi: 10.1121/1.4979055.

ISO/IEC (2008), ISO/IEC Guide 98-3:2008: Uncertainty of measurement. Part 3: Guide to the expression of uncertainty in measurement (GUM:1995).

Jagniatinskis A., Fiks B. (2014), Assessment of environmental noise from long-term window microphone measurements,Applied Acoustics, 76: 377-385, doi: 10.1016/j.apacoust.2013.09.007.

Liguori C., Ruggiero A., Russo D., Sommella P. (2017a), Estimation of the minimum measurement time interval in acoustic noise, Applied Acoustics, 127: 126-132, doi: 10.1016/j.apacoust.2017.05.032.

Liguori C., Ruggiero A., Russo D., Sommella P. (2017b), Innovative bootstrap approach for the estimation of minimum measurement time interval in road traffic noise evaluation, Measurement, 98: 237-242, doi: 10.1016/j.measurement.2016.12.008.

Makarewicz R. (2011a), Estimation of Lden for road-, aircraft-, and train noise, Acta Acustica united with Acustica, 97(3): 425–431, doi: 10.3813/AAA.918423.

Makarewicz R. (2011b), Uncertainty of approximation of the yearly average sound level of the road traffic noise, Acta Acustica united with Acustica, 97(3): 416–424, doi: 10.3813/AAA.918422.

Mateus M., Carrilho J.A.D., da Silva M.C.G. (2015), Assessing the influence of the sampling strategy on the uncertainty of environmental noise measurements through the bootstrap method, Applied Acoustics,

: 159–165, doi: 10.1016/j.apacoust.2014.09.021.

Pilch A. (2018), Sources of measurement uncertainty in determination of the directional diffusion coefficient value, Applied Acoustics, 129: 268–276, doi: 10.1016/j.apacoust.2017.07.016.

Przysucha B., Szelag A., Pawlik P. (2020), Probability distributions of one-day noise indicators in the process of the type A uncertainty evaluation of longterm noise indicators, Applied Acoustics, 161: 107158, doi: 10.1016/j.apacoust.2019.107158.

Romeu J., Jiménez S., Genescà M., Pàmies T., Capdevila R. (2006), Spatial sampling for night levels estimation in urban environments,Journal of the Acoustical Society of America, 120(2): 791–800, doi: 10.1121/1.2215219.

Ruggiero A., Russo D., Sommella P. (2016), Determining environmental noise measurement uncertainty in the context of the Italian legislative framework, Measurement, 93: 74-79, doi: 10.1016/j.measurement.2016.07.007.

Schomer P.D., DeVor R.E. (1981), Temporal sampling requirements for estimation of long-term average sound levels in the vicinity of airports,Journal of the Acoustical Society of America, 69(3):, 713–719, doi: 10.1121/1.385569.

Schumacher T., Straub D., Higgins C. (2012), Toward a probabilistic acoustic emission source location algorithm: A Bayesian approach, Journal of Sound and Vibration, 331(19): 4233–4245, doi: 10.1016/j.jsv.2012.04.028.

Stepien B. (2016), Confidence intervals for the longterm noise indicators using the kernel density estimator, Archives of Acoustics, 41(3): 517–525, doi: 10.1515/aoa-2016-0050.

Stępień B. (2017), Comparison of selected methods of the confidence intervals for long-term noise indicators, Acta Acustica united with Acustica, 103(2): 339–348, doi: 10.3813/AAA.919062.

Stępień B. (2018), A comparison of classical and Bayesian interval estimation for long-term indicators of road traffic noise, Acta Acustica united with Acustica, 104(6): 1118–1129, doi: 10.3813/AAA.919276.

Vos J. (2017), Estimating parameter values in a model for rating shooting sounds from field survey data, Journal of the Acoustical Society of America, 141(2): 864–877, doi: 10.1121/1.4976215.

DOI: 10.24425/aoa.2020.135249