Prediction of output response probability for sound environment system by introducing stochastic regression and fuzzy inference for simplified standard system model

Abstract

The traditional standard stochastic system models, such as the AR (Autoregressive), MA (Moving average) and ARMA (Autoregressive moving average) models, usually assume the Gaussian property for the fluctuation distribution. These models assume also the linear regression function for the time series of system input and output, and the well-known least squares method is applied based only on the linear correlation data. In the actual sound environment system, however, the stochastic process exhibits various non-Gaussian distributions, and there potentially exist various nonlinear correlations in addition to the linear correlation between input and output time series. Consequently, often the system input and output relationship in the actual phenomenon cannot be represented by a simple model such as the AR, MA and ARMA models. In this study, a prediction method of output response probability for sound environment system is derived by introducing a correction method for simplified standard system models. More precisely, a parameter-linear regression model is adopted as a simplified standard system model for the input and output relationship. Furthermore, a correction method for the simplified standard system model is proposed by introducing the stochastic regression and fuzzy inference. The proposed method is applied to the actual data in a sound environmnet system, and the practical usefulness is verified.