Assessment of several noise indicators are determined by the logarithmic mean <img src="/fulltext-image.asp?format=htmlnonpaginated&src=P42524002G141TV8_html\05_paper.gif" alt=""/>, from the sum of independent random results L1; L2; : : : ; Ln of the sound level, being under testing. The estimation of uncertainty of such averaging requires knowledge of probability distribution of the function form of their calculations. The developed solution, leading to the recurrent determination of the probability distribution function for the estimation of the mean value of noise levels and its variance, is shown in this paper.

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.

The authors focus their attention on the analysis of the probability density function of the equivalent noise level, in the context of a determination of the uncertainty of the obtained results in regard to the control of environmental acoustic hazards. In so doing, they discuss problems of correctness in the applicability of the classical normal distribution for the estimation of the expected interval value of the equivalent sound level. The authors also provide a set of procedures with respect to its derivation, based upon an assumption of the determined distribution of the measurement results. The obtained results then create the plane for the correct uncertainty calculation of the results of the determined controlled environmental acoustic hazard coefficient.

The assessment of the uncertainty of measurement results, an essential problem in environmental acoustic investigations, is undertaken in the paper. An attention is drawn to the - usually omitted - problem of the verification of assumptions related to using the classic methods of the confidence intervals estimation, for the controlled measuring quantity.

Especially the paper directs attention to the need of the verification of the assumption of the normal distribution of the measuring quantity set, being the base for the existing and binding procedures of the acoustic measurements assessment uncertainty. The essence of the undertaken problem concerns the binding legal and standard acts related to acoustic measurements and recommended in: 'Guide to the expression of uncertainty in measurement' (GUM) (OIML 1993), developed under the aegis of the International Bureau of Measures (BIPM). The model legitimacy of the hypothesis of the normal distribution of the measuring quantity set in acoustic measurements is discussed and supplemented by testing its likelihood on the environment acoustic results.

The Jarque-Bery test based on skewness and flattening (curtosis) distribution measures was used for the analysis of results verifying the assumption. This test allows for the simultaneous analysis of the deviation from the normal distribution caused both by its skewness and flattening. The performed experiments concerned analyses of the distribution of sound levels: LD, LE, LN, LDWN, being the basic noise indicators in assessments of the environment acoustic hazards.

When we look at the history of AGH – University of Science and Technology, recognized as one of the best universities in the country, we find that for that success many people worked for several dozen years. However, the subjects, the methodology and directions of their work were shaped by units – outstanding personalities of science. Just to mention, among others Professors Stanisław Zuber, Władysław Takliński, Witold Budryk, Maksymilian Tytus Huber and Władysław Bogusz. These people have shaped our institution, marked its new path of development and permanent place in the history of Polish and world science. To belong to such a group is a great ennoblement, for which one works out for his entire life. Undoubtedly, such personality was also Professor Zbigniew Witold Engel, to whom we said goodbye on November, 6th, 2013, in the St. Clement’s church in Wieliczka. Professor was born on April 1, 1933, in Zawady near Zhovkva in the province of Lviv. After graduating from Jan Matejko Middle and High School in Wieliczka in 1950 earned a matriculation certificate. Then he began his studies at the Department of Communications of Polytechnic Departments of Academy of Mining and Metallurgy and involved with our university for the next 63 years. October 1, 1952 the Department of Mechanics of the University of Mining and Metallurgy was created, and soon after began professor’s adventure that was the work of science, education and organization. The history and fate of our university are inextricably linked with the person of professor who practically since the very beginning of the Faculty supported it in all areas of its activities, and has always actively participated in academic life.

The acoustic climate assessment needed for the selection of solutions (technical, legal and organisational), which will help to minimise the acoustic hazards in the analysed areas, is realised on the basis of acoustic maps. The reference computational algorithms, assigned to them, require very thorough preparation of input data for the considered noise source model representing - in the best possible way - the acoustic climate. These input data are burdened with certain uncertainties in this class of computational tasks. The uncertainties are related to the problem of selecting proper argument values (from the interval of their possible variability) for the modelled processes. This situation has a direct influence on the uncertainty of acoustic maps.

The idea of applying the interval arithmetic for the assessment of acoustic models uncertainty is formulated in this paper. The computational formalism assigned to the interval arithmetic was discussed. The rules of interval estimations for the model solutions determining the sound level distribution around the analysed noise source - caused by possible errors in the input data - were presented. The application of this formalism was illustrated in uncertainty assessments of modelling acoustic influences of the railway noise linear source on the environment.

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.

The paper formulates some objections to the methods of evaluation of uncertainty in noise measurement which are presented in two standards: ISO 9612 (2009) and DIN 45641 (1990). In particular, it focuses on approximation of an equivalent sound level by a function which depends on the arithmetic average of sound levels. Depending on the nature of a random sample the exact value of the equivalent sound level may be significantly different from an approximate one, which might lead to erroneous estimation of the uncertainty of noise indicators. The article presents an analysis of this problem and the adequacy of the solution depending on the type of a random sample.