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Sampling techniques for the estimation of the annual equivalent noise level under urban traffic conditions
Applied Acoustics 64 (2003) 43–53 www.elsevier.com/locate/apacoust
Sampling techniques for the estimation of the annual equivalent noise level under urban traffic conditions E. Gajaa,*, A. Gimenezb,1, S. Sanchoa, A. Reiga a
Laboratorio de Ingenierı´a Acu´stica, E.T.S.I. Industriales, Universidad Polite´cnica de Valencia, Valencia, Spain b Departamento Proyectos, E.T. Disen˜o Industrial, Universidad Cardenal, Herrera-CEU, Moncada (Valencia), Spain Received 23 September 2001; received in revised form 27 June 2002; accepted 28 June 2002
Abstract This paper summarises 5 years of continuous noise measurements carried out at one of the most important squares in Valencia (Spain). The chosen square is a clear hotspot for traffic noise in a large city. The aim of this study is to determine the appropriate measuring time in order to obtain a 24-h noise level suitable to represent the annual equivalent level. Our findings allow us to reach a number of conclusions in terms of the most suitable urban traffic noise measurement techniques. A random day strategy for sampling is found to give a more accurate representation than a consecutive days strategy. If the sampling strategy involves measurements on randomly-chosen days, then at least 6 days should be used. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Urban traffic noise; Sampling techniques; Noise pollution
1. Introduction The objective of the European Parliament and Council Directive on the evaluation and management of noise is to establish a new framework in the E.U. to evaluate and manage noise exposure. The characteristics and repercussions of noise are analysed in the Green Book on Noise which obtained unsatisfactory results. In order to
* Corresponding author. Tel.: +34-963877524; fax: +34-963877179. E-mail addresses: egaja@fis.upv.es (E. Gaja), [email protected] (A. Gimenez). 1 Tel.: +34 961369000. 0003-682X/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0003-682X(02)00050-6
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improve this situation, this directive [1,12] is proposed to harmonise noise exposure evaluation methods among other factors. The proposal observes two preset indicators, LDEN (day–afternoon–night equivalent level) and Lnight (night equivalent level), the former being the basic indicator of noise as ‘‘disturbance’’ indicator. In all cases, each indicator is considered as the equivalent level of the corresponding specific period determined through all the periods in a year. With respect to measurement methods, the Green Book encourages the Member States to comply with the ISO 1996 regulations, part 1 and 2. These regulations specify that the long-term measuring time interval is the specific time that allows noise measurement results to be representative. It consists of a series of reference intervals, determined in order to describe environmental noise and commonly designated by the appropriate authority (ISO 1996/I Section 3.9 Ref. [11]). Later on, the section on the selection of measuring time intervals (ISO 1996/II Sections 5, 4, 3, Ref. [11]) illustrates how measuring time intervals will be chosen to ensure the appropriate coverage of all significant variations of noise emissions. Furthermore, measuring time interval selection will be such that the long-term average sound level or the long-term evaluation level will be determined with the necessary precision. Therefore, there is no specific methodology defined to evaluate long-term sound level, which allows for the selection of measuring time intervals provided that the mean long-term sound level is determined with the precision required Studying the contributions of several experts on the field, we observe that most of them estimate data statistics through data mean and standard deviation. Refs. [4–7] specifically refer to the statistical sampling values described for urban areas. References [2,8], offer a more detailed account of this data by obtaining the higher and lower limits for the equivalent level and the percentil levels for a 95% probability. Nevertheless, no prediction for these levels was performed and the statistical data was used to study dispersion and noise levels. Refs. [9,10] illustrate an attempt to evaluate the evolution of noise levels through statistical models (ARMA, ARIMA, SARIMA), as well as an attempt to predict in function of these, the levels that would be achieved with a given probability. Ref. [9], proposes a number of strategies with regard to the sample data to obtain precise data for a band [ 2, 3] dB of 95%.
2. Methodology Valencia City Hall has had an atmospheric pollution control network for several years. In fact, since 1994, a number of set monitors structure the City of Valencia’s Acoustic Pollution Vigilance and Prevention Network These monitors are connected to the Pollution Control Station, where real time data is stored. This program was financed by the Ministries of Public Works, Transports and Environment, in coordination with the E.U. Optimisation of Environmental Control Networks program. Bruel and Kjaer’s 2260 model sonometers were programmed to send out information on sound levels at 15 min intervals. The microphone was placed on a 4-m
E. Gaja et al. / Applied Acoustics 64 (2003) 43–53
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high pole in the centre of the square, complying with ISO 1996 regulations. The study is based on continuous measurements of 15-min equivalent continuous sound levels (LAeq, 15 m) throughout 5 years. The data were obtained from a monitor at Plaza de Espan˜a. This square is one of the most important hotspots of traffic in Valencia, since more than 150.000 vehicles of all kinds circulate through it (data obtained from the traffic control network, IMD 2000) 3. Results From the values obtained after 5 years of continuous measurements, the daily equivalent level (LAeq, 24 h) was obtained in the first place, with no corrections in
Fig. 1. LAeq,24 h variation in 1996.
Fig. 2. LAeq,24 h variation in 1998.
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terms of evening and night periods. The results illustrated the high sound level at the Plaza de Espan˜a, as well as its obvious seasonal aspect (already mentioned in several other studies, [13]) In fact, in Figs. 1 and 2 from years 1996 and 1998, the LAeq, 24h never indicated a quantity below 65 dB, and was next to always higher than 70 dB. Weekly cycles are clearly observed with a small decrease during the weekends (no leisure activities take place at the area during night time); August is the quietest month (summer holidays) and March is the noisiest, due to our Local Festival, Las Fallas, which takes place for four complete days (24 h a day) with a big profusion of jumping jacks and crackers. This anomalous acoustics will greatly affect the length of measurements carried out to obtain an annual representation. If we compare the measurements carried out during these 5 years by calculating each month’s equivalent level (Figs. 3 and 4), we will see that, except for some minor anomalies such as February 1997, the evolution of sound level remains unchanged.
Fig. 3. LAeq,month variation from 1996 to 2000.
Fig. 4. LAeq,year variation.
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Finally, the annual equivalent level for each year hardly presents a deviation, since the variation margin is lower than 1 dB.
4. Strategies With the data obtained from the 24-h equivalent level measurements (LAeq,24 h), an estimation is performed in terms of the error compared to the annual equivalent level value. To quantify the error incurred when shorter-than-yearly measurements are performed and to generalise to annual measurements, a series of initial strategies using statistical results and STATGRAPHIC PLUS V4,0 for Windows are presented. The strategies initially taken for this evaluation have been based on studies carried out by Schomer [9] and their follow ups carried out by Flindell and Gimenez [14]. These strategies are as follows:
a random day; 7 consecutive days; 14 consecutive days; 28 consecutive days; 7 random days; 28 random days; 2 random non-consecutive weeks within a year; 3 random non-consecutive weeks within a year; 4 random non-consecutive weeks within a year;
The methodology used for error evaluation in each of the strategies is as follows. Each of the strategies is considered independent from the others, taking 100 random samples per year for each strategy, which after 5 years resulted in a total amount of 500 samples. With each sample taken, the equivalent level of the period of each strategy is calculated and compared with the corresponding annual equivalent level of the sample extraction year. For example, for the 7-consecutive-days strategy, 100 samples were taken 7 consecutive days each year, and for each of these samples the equivalent level for these seven days was calculated. This value is compared with the annual equivalent level of the year in which the sample was taken. The differences between the data obtained with each strategy and the annual equivalent level are the values analysed. In this particular case, the values were 500,100 values per year. The statistics data obtained was; mean error value, typical deviation, probability of the data being included in a 1 dB range, and 90% probability band. The histograms obtained are of the following type (Figs. 5–7). Histograms represent the error measured in terms of the annual mean for each strategy. The frequency value shows the data found within the corresponding error range. The statistical data corresponding to each strategy is illustrated in Table 1
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Figs. 5–7. Frequency histogram of measured error for different strategies. Histograms represent the error measured in terms of the annual mean for each strategy. The frequency value shows the data found within the corresponding error range.
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The results for the random day selection strategy are more accurate than results obtained by the consecutive day selection strategy. In fact, if we compare the probability of staying in the [ 1; +1] dB range, for the 14 consecutive days strategy we would obtain a 76% probability, while for 14 random days we would obtain an 88% probability, and for 2 random weeks, that is 7 plus 7 non-consecutive days, the probability would be 76%. As we can see, the duration of measurements is clearly influenced by their continuity, since it includes measurements of working and leisure days with subsequent differences in acoustic characterisation. Another immediate conclusion obtained from these results is that the larger the number of days included in the strategy, the smaller the error and the higher the probability of data being in the 1 dB range. Nevertheless, this statement is not absolute, since some strategies do not render the expected results for the 90% probability range, e.g. 14 consecutive days compared to 28 consecutive days, since longer measurement periods can include a higher number of anomalous days among the randomly selected samples. Table 1 Statistics for different strategies Strategy 1 Day 7 Consecutive days 14 Consecutive days 28 Consecutive days 7 Random days 14 Random days 28 Random days 2 Random weeks 3 Random weeks 4 Random weeks
Mean 0.43 0.24 0.19 0.16 0 0.05 0.06 0.11 0.09 0.08
Standard deviation
Probability [ 1;+1]
Band 90% probability
1.76 1.46 1.28 1.14 1.05 0.75 0.53 1.07 0.948 0.81
53.8% 66% 70.2% 67.6% 81% 88% 93.2 76% 84% 85.8%
[ [ [ [ [ [ [ [ [ [
Fig. 8. Box-and-whisker plot for 14 consecutive days strategy.
3.2;1.79] 2.28;1.85] 2.4;2.1] 1.7;2.5] 1.12;2.41] 0.9;1.6] 0.73;1.1] 1.32;1.85] 1.17;2.27] 0.98;1.79]
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For example, a comparison of the 14 and 18 consecutive days strategies observes the higher limit for 28 continuous days to be above the limit for 14 continuous days, when higher accuracy was, in fact, the aim (2.5 dB limit for 28 days and 2.1 dB for 14 days). At the same time, this inaccuracy does not occur in terms of lower limits (see Table 1). This is due to more anomalous days included in the random samples selected. As we can see in the Box-Whiskers diagram for the 28 consecutive days sample (see Fig. 9) there is a high number of anomalous data for positive errors, when compared to the 14 days strategy (Fig. 8). However, the two strategies contain equal anomalous data in terms of negative errors. This causes an increase in the higher limit that would not take place should the presence of anomalous data be the same for both strategies.
Fig. 9. Box-and-whisker plot for 28 consecutive days strategy.
Table 2 Statistics for consecutive days Strategy 2 Consecutive days 3 Consecutive days 4 Consecutive days 5 Consecutive days 6 Consecutive days 7 Consecutive days 8 Consecutive days 9 Consecutive days 10 Consecutive days 11 Consecutive days 12 Consecutive days 13 Consecutive days 14 Consecutive days
Mean 0.44 0.34 0.27 0.21 0.31 0.19 0.24 0.21 0.31 0.21 0.23 0.19 0.19
Standard deviation
Probability [ 1;+1]
Probability [ 2;+2]
Probability [ 3;+3]
90% Probability range
1.53 1.41 1.42 1.43 1.21 1.31 1.46 1.3 1.19 1.26 1.35 1.31 1.28
55% 58% 66% 70% 71% 69% 66% 70% 71% 71% 69% 69% 70%
83% 86% 90% 90% 91% 90% 87% 91% 93% 92% 87% 89% 89%
94% 95% 97% 96% 98% 97% 95% 96% 98% 97% 96% 95% 96%
[ [ [ [ [ [ [ [ [ [ [ [ [
2.77;1.6] 2.38;1.65] 2.12;1.58] 2;2.11] 2.2;1.38] 2;1.87] 2.21 ; 1.91] 2;1.53] 1.95;1.15] 1.81;1.51] 2.37;2.18] 2.08;2.03] 2.4;2.1]
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Once the results have been evaluated, the annual mean can be estimated according to two strategies, continuous measurement or random measurement, for periods of time under 14 days. The results obtained for each case are illustrated in Table 2; furthermore, the probability for 2 and 3 dB ranges can be incorporated into the statistics. Table 3 Statistics for random days Strategy 2 Random days 3 Random days 4 Random days 5 Random days 6 Random days 7 Random days 8 Random days 9 Random days 10 Random days 11 Random days 12 Random days 13 Random days 14 Random days
Mean 0.19 0.26 0.21 0.14 0.23 0 0.05 0.12 0.13 0.07 0.07 0.05 0.05
Standard deviation
Probability [ 1;+1]
Probability [ 2;+2]
Probability [ 3;+3]
90% Probability range
1.62 1.02 0.93 1.04 0.8 1.05 0.97 0.79 0.72 0.84 0.73 0.73 0.75
66% 75% 80% 77% 84% 81% 80% 87% 86% 86% 87% 88% 88%
87% 95% 97% 94% 96% 93% 95% 98% 98% 96% 98% 97% 96%
93% 97% 98% 97% 99% 97% 98% 99% 100% 99% 99% 100% 99%
[ [ [ [ [ [ [ [ [ [ [ [ [
2.46;1.76] 1.77;1.05] 1.54;0.96] 1;44;1.82] 1.33;1.16] 1.12;2.41] 1.17;1.94] 1.08;1.3] 1.03;1.61] 1.03;1.62] 0.95;1.37] 0.87;1.47] 0.9;1.6]
Fig. 10 and 11. These represent the 1, 2, 3 dB range probability for a different number of days for random and continuous days strategies.
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Fig. 12. Comparison of 1 probability for continuous and random strategies.
In sight of these results and the need for accuracy, the random day strategy proves best, although for the 3 dB range, both strategies obtain similar accuracy levels as long as enough number of days is considered. However, several peculiarities must be considered. Analysing the probability of obtaining the LAeq,annual in the [ 1,+1] dB range for both strategies, and according to Figs. 10 and 11, and the data in Tables 2 and 3, we can see that for both strategies (continuous days and random days) the value is stabilized round 9 days for the [ 1; +1] dB range. Nevertheless, this stabilization is best illustrated by the random days strategy, as seen in Fig. 12. This is due to the increased number of days measured for the consecutive days strategy, which multiply the possibility of having two weekends and a larger number of anomalies included in the samples. If we observe Table 2, for the 90% range, the higher and lower limits are increased with respect to the previous strategies. The samples observe a higher number of anomalous days with respect to the former strategies.
5. Conclusions The results obtained indicate it is possible to determine the 24-h equivalent level representative of the equivalent annual level by means of sampling. In fact, after establishing the random days strategy as the best to obtain accurate results, the number of days needed to maintain this accuracy is considered to be 9, with a 87, 98 an 99% accuracy conditional on the possibility to determine it within the 1, 2, 3 dB range. Satisfactory results are obtained if an 87% probability is achieved in the 1 dB band, with a typical deviation of 0.79 dB, and a 90% probability of the LAeq,24 h being in the [ 1.08, 1.3] range with respect to the annual value. However, in order to reduce the number of days measured, the 6 random days option is advocated, since it renders more accurate results (giving between 84, 96 and 99% probability of being within 1. 2, 3 dB range) than intermediate options (7 or 8 random days)
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Acknowledgements We want to express our gratitude towards Valencia City Hall Environmental Laboratory for the facilities provided for the development of this work, as well as other previous works.
References [1] Comisio´n de las comunidades europeas. Polı´tica futura de lucha contra el ruido. ISBN 92-78-107263; 1996. [2] Bjo¨rk EA. Community noise in different seasons in Kuopio, Finland. Applied Acoustics 1994;42: 137–50. [4] Bartolini R, Bisio G, Magrini U. The acoustic mapping of Genoa—the relative weight of the various noise sources and the spatial distribution of outdoor noise levels. Noise Control Engineering Journal 1990;34:9–15. [5] Utley WA. Descriptors for ambient noise. Proceedings of InterNoise 1985;85:1069–72. [6] Bisio G, Magrini A. Acoustic survey of the noise levels in a middle size town—the influence of some traffic restriccions. Proceedings of InterNoise 1992;92:861–4. [7] Bisio G, Fichera L, Marletta L, Miroglio D. Temporal distributions of outdoor noise levels in densely built-up areas. Proceedings of InterNoise 1996;96:2025–8. [8] Boullosa RR, Perez Ruiz SJ. An exploratory study of community noise levels in Mexico City. Applied Acoustics 1987;22:271–80. [9] Schomer P. D., DeVor R. E., Temporal sampling requirements for estimation of long-term average sound levels in the vicinity of airports. J Acoust Soc Am 69(3) 713–19. [10] Machimbarrena Gutierrez M, Turin˜o Vaca A, Gonza´lez Sua´rez J, Sa´nchez Rivera JI, Valseros Blanco MoC. The seasonal nature of urban noise: a case of study. Proceedings of Internoise 1997;97: 839–42. [11] ISO 1996. Description and measurement of environmental noise; 1982. [12] Europe Comunity Comission. Propuesta de directiva del parlamento Europeo y del consejo sobre evaluaco´n y gestio´n del ruido ambiental; 2000. [13] Reig A., Gaja E., Sancho S., Manglano J.L., Measuring the traffic noise in Valencia. Proceedings of ICA-ASA; 1998. [14] Flindell IH, Gime´nez A. Sampling requirements for estimating LAeq,annual by the method of measurement. International Erasmus Project. Institute of Sound and Vibration. University of Southampton; 1999.
Sampling techniques for the estimation of the annual equivalent noise level under urban traffic conditions E. Gajaa,*, A. Gimenezb,1, S. Sanchoa, A. Reiga a
Laboratorio de Ingenierı´a Acu´stica, E.T.S.I. Industriales, Universidad Polite´cnica de Valencia, Valencia, Spain b Departamento Proyectos, E.T. Disen˜o Industrial, Universidad Cardenal, Herrera-CEU, Moncada (Valencia), Spain Received 23 September 2001; received in revised form 27 June 2002; accepted 28 June 2002
Abstract This paper summarises 5 years of continuous noise measurements carried out at one of the most important squares in Valencia (Spain). The chosen square is a clear hotspot for traffic noise in a large city. The aim of this study is to determine the appropriate measuring time in order to obtain a 24-h noise level suitable to represent the annual equivalent level. Our findings allow us to reach a number of conclusions in terms of the most suitable urban traffic noise measurement techniques. A random day strategy for sampling is found to give a more accurate representation than a consecutive days strategy. If the sampling strategy involves measurements on randomly-chosen days, then at least 6 days should be used. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Urban traffic noise; Sampling techniques; Noise pollution
1. Introduction The objective of the European Parliament and Council Directive on the evaluation and management of noise is to establish a new framework in the E.U. to evaluate and manage noise exposure. The characteristics and repercussions of noise are analysed in the Green Book on Noise which obtained unsatisfactory results. In order to
* Corresponding author. Tel.: +34-963877524; fax: +34-963877179. E-mail addresses: egaja@fis.upv.es (E. Gaja), [email protected] (A. Gimenez). 1 Tel.: +34 961369000. 0003-682X/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0003-682X(02)00050-6
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improve this situation, this directive [1,12] is proposed to harmonise noise exposure evaluation methods among other factors. The proposal observes two preset indicators, LDEN (day–afternoon–night equivalent level) and Lnight (night equivalent level), the former being the basic indicator of noise as ‘‘disturbance’’ indicator. In all cases, each indicator is considered as the equivalent level of the corresponding specific period determined through all the periods in a year. With respect to measurement methods, the Green Book encourages the Member States to comply with the ISO 1996 regulations, part 1 and 2. These regulations specify that the long-term measuring time interval is the specific time that allows noise measurement results to be representative. It consists of a series of reference intervals, determined in order to describe environmental noise and commonly designated by the appropriate authority (ISO 1996/I Section 3.9 Ref. [11]). Later on, the section on the selection of measuring time intervals (ISO 1996/II Sections 5, 4, 3, Ref. [11]) illustrates how measuring time intervals will be chosen to ensure the appropriate coverage of all significant variations of noise emissions. Furthermore, measuring time interval selection will be such that the long-term average sound level or the long-term evaluation level will be determined with the necessary precision. Therefore, there is no specific methodology defined to evaluate long-term sound level, which allows for the selection of measuring time intervals provided that the mean long-term sound level is determined with the precision required Studying the contributions of several experts on the field, we observe that most of them estimate data statistics through data mean and standard deviation. Refs. [4–7] specifically refer to the statistical sampling values described for urban areas. References [2,8], offer a more detailed account of this data by obtaining the higher and lower limits for the equivalent level and the percentil levels for a 95% probability. Nevertheless, no prediction for these levels was performed and the statistical data was used to study dispersion and noise levels. Refs. [9,10] illustrate an attempt to evaluate the evolution of noise levels through statistical models (ARMA, ARIMA, SARIMA), as well as an attempt to predict in function of these, the levels that would be achieved with a given probability. Ref. [9], proposes a number of strategies with regard to the sample data to obtain precise data for a band [ 2, 3] dB of 95%.
2. Methodology Valencia City Hall has had an atmospheric pollution control network for several years. In fact, since 1994, a number of set monitors structure the City of Valencia’s Acoustic Pollution Vigilance and Prevention Network These monitors are connected to the Pollution Control Station, where real time data is stored. This program was financed by the Ministries of Public Works, Transports and Environment, in coordination with the E.U. Optimisation of Environmental Control Networks program. Bruel and Kjaer’s 2260 model sonometers were programmed to send out information on sound levels at 15 min intervals. The microphone was placed on a 4-m
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high pole in the centre of the square, complying with ISO 1996 regulations. The study is based on continuous measurements of 15-min equivalent continuous sound levels (LAeq, 15 m) throughout 5 years. The data were obtained from a monitor at Plaza de Espan˜a. This square is one of the most important hotspots of traffic in Valencia, since more than 150.000 vehicles of all kinds circulate through it (data obtained from the traffic control network, IMD 2000) 3. Results From the values obtained after 5 years of continuous measurements, the daily equivalent level (LAeq, 24 h) was obtained in the first place, with no corrections in
Fig. 1. LAeq,24 h variation in 1996.
Fig. 2. LAeq,24 h variation in 1998.
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terms of evening and night periods. The results illustrated the high sound level at the Plaza de Espan˜a, as well as its obvious seasonal aspect (already mentioned in several other studies, [13]) In fact, in Figs. 1 and 2 from years 1996 and 1998, the LAeq, 24h never indicated a quantity below 65 dB, and was next to always higher than 70 dB. Weekly cycles are clearly observed with a small decrease during the weekends (no leisure activities take place at the area during night time); August is the quietest month (summer holidays) and March is the noisiest, due to our Local Festival, Las Fallas, which takes place for four complete days (24 h a day) with a big profusion of jumping jacks and crackers. This anomalous acoustics will greatly affect the length of measurements carried out to obtain an annual representation. If we compare the measurements carried out during these 5 years by calculating each month’s equivalent level (Figs. 3 and 4), we will see that, except for some minor anomalies such as February 1997, the evolution of sound level remains unchanged.
Fig. 3. LAeq,month variation from 1996 to 2000.
Fig. 4. LAeq,year variation.
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Finally, the annual equivalent level for each year hardly presents a deviation, since the variation margin is lower than 1 dB.
4. Strategies With the data obtained from the 24-h equivalent level measurements (LAeq,24 h), an estimation is performed in terms of the error compared to the annual equivalent level value. To quantify the error incurred when shorter-than-yearly measurements are performed and to generalise to annual measurements, a series of initial strategies using statistical results and STATGRAPHIC PLUS V4,0 for Windows are presented. The strategies initially taken for this evaluation have been based on studies carried out by Schomer [9] and their follow ups carried out by Flindell and Gimenez [14]. These strategies are as follows:
a random day; 7 consecutive days; 14 consecutive days; 28 consecutive days; 7 random days; 28 random days; 2 random non-consecutive weeks within a year; 3 random non-consecutive weeks within a year; 4 random non-consecutive weeks within a year;
The methodology used for error evaluation in each of the strategies is as follows. Each of the strategies is considered independent from the others, taking 100 random samples per year for each strategy, which after 5 years resulted in a total amount of 500 samples. With each sample taken, the equivalent level of the period of each strategy is calculated and compared with the corresponding annual equivalent level of the sample extraction year. For example, for the 7-consecutive-days strategy, 100 samples were taken 7 consecutive days each year, and for each of these samples the equivalent level for these seven days was calculated. This value is compared with the annual equivalent level of the year in which the sample was taken. The differences between the data obtained with each strategy and the annual equivalent level are the values analysed. In this particular case, the values were 500,100 values per year. The statistics data obtained was; mean error value, typical deviation, probability of the data being included in a 1 dB range, and 90% probability band. The histograms obtained are of the following type (Figs. 5–7). Histograms represent the error measured in terms of the annual mean for each strategy. The frequency value shows the data found within the corresponding error range. The statistical data corresponding to each strategy is illustrated in Table 1
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Figs. 5–7. Frequency histogram of measured error for different strategies. Histograms represent the error measured in terms of the annual mean for each strategy. The frequency value shows the data found within the corresponding error range.
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The results for the random day selection strategy are more accurate than results obtained by the consecutive day selection strategy. In fact, if we compare the probability of staying in the [ 1; +1] dB range, for the 14 consecutive days strategy we would obtain a 76% probability, while for 14 random days we would obtain an 88% probability, and for 2 random weeks, that is 7 plus 7 non-consecutive days, the probability would be 76%. As we can see, the duration of measurements is clearly influenced by their continuity, since it includes measurements of working and leisure days with subsequent differences in acoustic characterisation. Another immediate conclusion obtained from these results is that the larger the number of days included in the strategy, the smaller the error and the higher the probability of data being in the 1 dB range. Nevertheless, this statement is not absolute, since some strategies do not render the expected results for the 90% probability range, e.g. 14 consecutive days compared to 28 consecutive days, since longer measurement periods can include a higher number of anomalous days among the randomly selected samples. Table 1 Statistics for different strategies Strategy 1 Day 7 Consecutive days 14 Consecutive days 28 Consecutive days 7 Random days 14 Random days 28 Random days 2 Random weeks 3 Random weeks 4 Random weeks
Mean 0.43 0.24 0.19 0.16 0 0.05 0.06 0.11 0.09 0.08
Standard deviation
Probability [ 1;+1]
Band 90% probability
1.76 1.46 1.28 1.14 1.05 0.75 0.53 1.07 0.948 0.81
53.8% 66% 70.2% 67.6% 81% 88% 93.2 76% 84% 85.8%
[ [ [ [ [ [ [ [ [ [
Fig. 8. Box-and-whisker plot for 14 consecutive days strategy.
3.2;1.79] 2.28;1.85] 2.4;2.1] 1.7;2.5] 1.12;2.41] 0.9;1.6] 0.73;1.1] 1.32;1.85] 1.17;2.27] 0.98;1.79]
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For example, a comparison of the 14 and 18 consecutive days strategies observes the higher limit for 28 continuous days to be above the limit for 14 continuous days, when higher accuracy was, in fact, the aim (2.5 dB limit for 28 days and 2.1 dB for 14 days). At the same time, this inaccuracy does not occur in terms of lower limits (see Table 1). This is due to more anomalous days included in the random samples selected. As we can see in the Box-Whiskers diagram for the 28 consecutive days sample (see Fig. 9) there is a high number of anomalous data for positive errors, when compared to the 14 days strategy (Fig. 8). However, the two strategies contain equal anomalous data in terms of negative errors. This causes an increase in the higher limit that would not take place should the presence of anomalous data be the same for both strategies.
Fig. 9. Box-and-whisker plot for 28 consecutive days strategy.
Table 2 Statistics for consecutive days Strategy 2 Consecutive days 3 Consecutive days 4 Consecutive days 5 Consecutive days 6 Consecutive days 7 Consecutive days 8 Consecutive days 9 Consecutive days 10 Consecutive days 11 Consecutive days 12 Consecutive days 13 Consecutive days 14 Consecutive days
Mean 0.44 0.34 0.27 0.21 0.31 0.19 0.24 0.21 0.31 0.21 0.23 0.19 0.19
Standard deviation
Probability [ 1;+1]
Probability [ 2;+2]
Probability [ 3;+3]
90% Probability range
1.53 1.41 1.42 1.43 1.21 1.31 1.46 1.3 1.19 1.26 1.35 1.31 1.28
55% 58% 66% 70% 71% 69% 66% 70% 71% 71% 69% 69% 70%
83% 86% 90% 90% 91% 90% 87% 91% 93% 92% 87% 89% 89%
94% 95% 97% 96% 98% 97% 95% 96% 98% 97% 96% 95% 96%
[ [ [ [ [ [ [ [ [ [ [ [ [
2.77;1.6] 2.38;1.65] 2.12;1.58] 2;2.11] 2.2;1.38] 2;1.87] 2.21 ; 1.91] 2;1.53] 1.95;1.15] 1.81;1.51] 2.37;2.18] 2.08;2.03] 2.4;2.1]
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Once the results have been evaluated, the annual mean can be estimated according to two strategies, continuous measurement or random measurement, for periods of time under 14 days. The results obtained for each case are illustrated in Table 2; furthermore, the probability for 2 and 3 dB ranges can be incorporated into the statistics. Table 3 Statistics for random days Strategy 2 Random days 3 Random days 4 Random days 5 Random days 6 Random days 7 Random days 8 Random days 9 Random days 10 Random days 11 Random days 12 Random days 13 Random days 14 Random days
Mean 0.19 0.26 0.21 0.14 0.23 0 0.05 0.12 0.13 0.07 0.07 0.05 0.05
Standard deviation
Probability [ 1;+1]
Probability [ 2;+2]
Probability [ 3;+3]
90% Probability range
1.62 1.02 0.93 1.04 0.8 1.05 0.97 0.79 0.72 0.84 0.73 0.73 0.75
66% 75% 80% 77% 84% 81% 80% 87% 86% 86% 87% 88% 88%
87% 95% 97% 94% 96% 93% 95% 98% 98% 96% 98% 97% 96%
93% 97% 98% 97% 99% 97% 98% 99% 100% 99% 99% 100% 99%
[ [ [ [ [ [ [ [ [ [ [ [ [
2.46;1.76] 1.77;1.05] 1.54;0.96] 1;44;1.82] 1.33;1.16] 1.12;2.41] 1.17;1.94] 1.08;1.3] 1.03;1.61] 1.03;1.62] 0.95;1.37] 0.87;1.47] 0.9;1.6]
Fig. 10 and 11. These represent the 1, 2, 3 dB range probability for a different number of days for random and continuous days strategies.
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Fig. 12. Comparison of 1 probability for continuous and random strategies.
In sight of these results and the need for accuracy, the random day strategy proves best, although for the 3 dB range, both strategies obtain similar accuracy levels as long as enough number of days is considered. However, several peculiarities must be considered. Analysing the probability of obtaining the LAeq,annual in the [ 1,+1] dB range for both strategies, and according to Figs. 10 and 11, and the data in Tables 2 and 3, we can see that for both strategies (continuous days and random days) the value is stabilized round 9 days for the [ 1; +1] dB range. Nevertheless, this stabilization is best illustrated by the random days strategy, as seen in Fig. 12. This is due to the increased number of days measured for the consecutive days strategy, which multiply the possibility of having two weekends and a larger number of anomalies included in the samples. If we observe Table 2, for the 90% range, the higher and lower limits are increased with respect to the previous strategies. The samples observe a higher number of anomalous days with respect to the former strategies.
5. Conclusions The results obtained indicate it is possible to determine the 24-h equivalent level representative of the equivalent annual level by means of sampling. In fact, after establishing the random days strategy as the best to obtain accurate results, the number of days needed to maintain this accuracy is considered to be 9, with a 87, 98 an 99% accuracy conditional on the possibility to determine it within the 1, 2, 3 dB range. Satisfactory results are obtained if an 87% probability is achieved in the 1 dB band, with a typical deviation of 0.79 dB, and a 90% probability of the LAeq,24 h being in the [ 1.08, 1.3] range with respect to the annual value. However, in order to reduce the number of days measured, the 6 random days option is advocated, since it renders more accurate results (giving between 84, 96 and 99% probability of being within 1. 2, 3 dB range) than intermediate options (7 or 8 random days)
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Acknowledgements We want to express our gratitude towards Valencia City Hall Environmental Laboratory for the facilities provided for the development of this work, as well as other previous works.
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