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Abstract

The function of a new estimation procedure of long-term noise indicators is considered in this study. New possibilities are related to the stochastic modelling of the control data formation mechanism. Assuming the mathematical formalism based on the adaptive model of exponential smoothing of control data, the need of controlling at each estimation stage of long-term noise indicators, the adherence to the model assumptions is formulated. The procedure of its realisation is described in the paper. The tracking signal method referred to the tested errors of the assumed model was applied. The ratio of the sum of model errors in relation to the average absolute error, generated by the assumed approximation, was selected as the representative of the tracking signal. Conditions for the acceptation of the model assumption were defined. The analysis of functionality of the developed solution was illustrated by the results of a continuous noise monitoring recorded at one of the main arteries in Kraków.

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Authors and Affiliations

Wojciech Batko
Renata Bal
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Abstract

The problem of estimation of the long-term environmental noise hazard indicators and their uncertainty is presented in the present paper. The type A standard uncertainty is defined by the standard deviation of the mean. The rules given in the ISO/IEC Guide 98 are used in the calculations. It is usually determined by means of the classic variance estimators, under the following assumptions: the normality of measurements results, adequate sample size, lack of correlation between elements of the sample and observation equivalence. However, such assumptions in relation to the acoustic measurements are rather questionable. This is the reason why the authors indicated the necessity of implementation of non-classical statistical solutions. An estimation idea of seeking density function of long-term noise indicators distribution by the kernel density estimation, bootstrap method and Bayesian inference have been formulated. These methods do not generate limitations for form and properties of analyzed statistics. The theoretical basis of the proposed methods is presented in this paper as well as an example of calculation process of expected value and variance of long-term noise indicators LDEN and LN. The illustration of indicated solutions and their usefulness analysis were constant due to monitoring results of traffic noise recorded in Cracow, Poland.
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Authors and Affiliations

Wojciech Michał Batko
Bartłomiej Stępień
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Abstract

A non-classical model of interval estimation based on the kernel density estimator is presented in this paper. This model has been compared with interval estimation algorithms of the classical (parametric) statistics assuming that the standard deviation of the population is either known or unknown. The non-classical model does not have to assume belonging of random sample to a normal distribution. A theoretical basis of the proposed model is presented as well as an example of calculation process which makes possible determining confidence intervals of the expected value of long-term noise indicators Aden and LN. The statistical analysis was carried out for 95% interval widths obtained by using each of these models. The inference of their usefulness was performed on the basis of results of non-parametric statistical tests at significance level α = 0.05. The data used to illustrate the proposed solutions and carry out the analysis were results of continuous monitoring of traffic noise recorded in 2004 in one of the main arteries of Krakow in Poland.

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Authors and Affiliations

Bartłomiej Stępień
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Abstract

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.

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Authors and Affiliations

Bartłomiej Stępień

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