This paper describes a trial of evaluating the proper characteristics of multiple sound insulatain systems from their output responses contaminated by unknown background noises. The unknown parameters of sound insulation systems are first estimated on the basis of hte linear time series on an intensity scale, describing functionally the input-output relation of the systems. Then, their output probability distributions are predicted when an arbitrary input noise passes through these insulation systems.

A new trial of statistical evaluation for an output response of power linear type acoustic systems with nonstationary random input is proposed. The purpose of this study is to predict the output probability distribution function on the basis of a standard type pre-experiment in a laboratoty. The statistical properties like nonstationarity, non-Gamma distribution property and various type linear and non-linear correlations of input signal are reflected in the form of differential operation with respect to distribution parameters. More concretely, the pre-experiment is carried out for a power linear acoustic system excited only by the Gamma distribution type sandard random input. Considering the non-negative random property for the output response of a power linear system, the well-known statistical Laguerre expansion series type probability expression is first employed as the framework of basic probability distribution expression on the output power fluctuation. Then, the objective output probability distribution for a non-stationary case can be easily derived only by successively employing newly introduced differential operators to this basic probability distribution of statistical Laguerre expansion series type. As an application to the actual noise environment, the proposed method is employed for an evaluation problem on the stochastic response probability distribution for an acoustic sound insulation system excited by a nonstationary input noise.