Abstract
Obviously a random process that may be considered as strictly stationary seldom exists in practical random phenomena such as urban noises. Especially, the road traffic noise always exhibits, the nonstationary property in a long time interval, because of the temporal changes of social or urban environment. In addition to such an essential cause, taking into consideration the extensiveness of collected noise data in a long time interval (for example, observed by an automatically recording sound-level meter), the complexity of statistical treatment involved and the capacity of digital computer, we are inevitably requited to use observed data skillfully with computer for the prediction and/or estimation problem of state variables in a nonstationary urban noise.
In this paper, concerning the actual road traffic noise with many different types of level distributions, a new trial of statistical treatment to estimate the noise level distribution in a Long time interval on the basis of an information of noise level statistics (with high degree of experimental reliability) in a short time interval is firstly considered from the theoretical view-point. That is, the above estimation technique is mainly founded on the use of the newly established probability expression in the form of statistical expansion series. The expression has an arbitrary number of nonstationary-parameters to be universally available for arbitrary nonstationary forms of the traffic noise fluctuation over a long period of time. More explicitly, in this unified expression, the stationary term is taken in the first term and many nonstationary factors are reflected successively in the second and higher order expansion terms. Two explicit, expressions of level distributions over a long time interval on the basis of level distribution over a short time interval are derived. This is a special application of the above general theory. In the derivatibn, two fundamental and typical viewpoints of modeling an actual random time series are pointed out. One is to regard the time series as multiplicable, and the other is to rigard it as additive. Finally, the validity of the above estimation theory is experimentally confirmed by applying it to data of actually measured road traffic noise. The experimental result is in good agreement with the theory.
