上位レベルにおける騒音・振動分布の予測とL_α値の簡易評価法

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In general, it is well-known that the distribution function within a higher fluctuation range can reflect the evaluation of human response and the individual characteristics of noise and vibration, so that it is more important than that within a lower fluctuation range in the field of the evaluation of industrial and road traffic noise. From this point view, this paper provides the method of statistical treatment of random noise or vibration which is suitable to the estimation of the level distribution within a higher fluctuation range and a simplified evaluation procedure of the higher L_α sound level, by introducing the idea of conditional distribution function. In the previous paper, we have reported on some trials of the statistical treatment for the digital level fluctuation of arbitrary random noise or vibration, when the random noise or vibration with the level, Z, of arbitrary distribution type is considered as a sum of two different random processes, X and U, with the digital level based on the naturalinternal structure or analytically artificial classification of fluctuation. Let us now introduce an arbitrary function, (Z), and consider its expectation value, Eq. (1). Equations (3) and (4) can be obtained by using the backward Newton's interpolate formula. Our main problem is how to derive the probability function, P(Z), in the difference form expanded into series based on the statistical informations of X and U. After somewhat complicated calculation, we obtain the two expressions expanded into series, Eqs. (11) and (13), when X is statistically correlated with U;Eqs. (14) and (15), when X is statistically independent of U. Though the theoretical development in this paper seems to be similar to the previous method, we would like to emphasize the fact that the resultant expressions are different forming striking contrast with the previous results. Namely, in comparison with the probability density or distribution functions in the previous paper, Eqs. (14) and (15) are the theoretical expressions based on the forward difference formula, being different from the previous statical treatment. Therefore, these theoretical expression are very suitable to the estimation of the level probability distribution within a higher fluctuation range. We have experimentally confirmed the validity of our theory by means of not only digital simulation, but also the experimentally observed city noise data given by Dr. Morita and the road traffic noise data in Hiroshima City. The result of experimental study are shown in Figs. 1 through 7. Equation (22) is the conditional distribution expression that is introduced for the purpose of the effective processing of experimentally observed data (see Fig. 4). With the aid of this expression, the long time level distribution can be easily predicted from the short time level distribution within the higher fluctuation range by using only a part of all observed data. The corresponding experimental results are shown in Figs. 6 and 7. The above statistical treatment is characterized by the following points:(1) The resultant expression are given in the form of the difference type, so that the frequency distribution, P_(X), can be utilized keeping the experimentally observed data in their crude numerical form without making continuous level fitting;(2) In the special case when the level width h=d, approaches to 0, the above theoretical expression exactly agrees with the expression reported previously in the continuous level form;(3) Since the present theory is suitable to the stimation of the level distribution within the higher fluctuation range and the prediction of the higher L_α sound level, the proposed statistical treatment can be used to such random noise and vibration showing various distribution types on the basis of the flexibility and universal validity of the theoretical expression;(4)By using the conditional distribution function which is based on the conditional data collection, this th
社団法人日本音響学会の論文
1978-05-01

上位レベルにおける騒音・振動分布の予測とL_α値の簡易評価法

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