エネルギー加算則の一般化と合成騒音・振動に関する分布予測への一組織的適用

抄録

As is well-known, in the practical evaluation and control of the environmental noise and vibration, the principle on an additivity property for energy is widely applied not only to the deterministic signal but also to the stochastic signal. Originally, this principle is effective only in the averaged form of signal fluctuation, and so it is essentially impossible to explain sufficiently every sides of the variety and complexity of actual random phenomena only by use of this fundamental principle. Accordingly, it is fundamentally necessary to find out in a generalized form of the above principle some new type of an additivity rule applicable not only to the first order statistic (i. e. , mean value) but also to the higher order statistical information for various types of actual fluctuation form. In this paper, a new trial toward the statistical prediction for the total probability distribution form of a combined vibration or noise level fluctuations emitted from two different sources is hierarchically proposed from a generalized viewpoint based on the additivity property of arbitrary order cumulant statistics. More concretely, though the probability distribution of combined vibration or noise level fluctuations can be theoretically predicted in two statistical expansion expression form of Hermite and Laguerre series types, its expansion coefficients and statistical properties can be systematically derived in the recursive algorithm styles by use of the proposed general additive principle. Finally, after once the legitimacy of the present theory is confirmed by means of digital simulation technique, the effectiveness of this prediction method is experimentally confirmed too by applying it to the actual data of vibration and noise level fluctuations observed in a large city.