Probabilistic modelling of the temporal variability of urban sound levels

Relying on monitoring networks to compute or improve noise maps is an increasingly used approach. To be able to use this approach to provide adequate temporal treatments, a good understanding of the temporal variations within urban sound level time series is required. This paper provides an in-depth statistical analysis of the temporal characteristics of urban sound environments, on the basis of a wide measurement campaign during 8 month, at 23 measurement stations in Paris, which cover a large variety of urban sound environments. The time series of sound levels were recorded continuously with a 125 ms-time resolution, from which LA(50,1h) values were extracted. In total, 72 time-slots of interest are defined (24 1h-periods covering all days of the week). The statistical analysis determines for each station the Daily Average Noise Pattern (DANP), and for each of the 72 time-slots the 1h-Generalized Extreme Values distributions. The Generalized Extreme Values distributions are found to outperform the normal distributions to model the LA(50,1h) distributions. In addition, the average sound level differences between these 72 1h-time periods are calculated along with their variability, resulting in 72x72 delta matrices that describe the temporal relations between sound levels. This database is then used to develop two models, which aim to estimate DANP based on a limited amount of measurements. The model M1 relies on the delta matrices, whereas the model M2 consists of a weighted average of the DANP that are stored in the database in which the weights are based upon measures of similarity between the stations. Both models rely on probability density functions, and provide a measure for the reliability of the estimated noise levels. A test of both modelling approaches through simulated measurements shows that the model M1 seems to be more robust in case measurements are inaccurate. Beyond these two models, the proposed database could serve in the development of further models that aim to estimate sound levels based on a limited amount of measurements