Abstract
The traditional standard stochastic system models, such as the autoregressive (AR), moving average (MA) and autoregressive moving average (ARMA) models, usually assume the Gaussian property for the fluctuation distribution, and the well-known least squares method is applied on the basis of only the linear correlation data. In the actual sound environment system, the stochastic process exhibits various non-Gaussian distributions, and there exist potentially various nonlinear correlations in addition to the linear correlation between input and output time series. Consequently, the system input and output relationship in the actual phenomenon cannot be represented by a simple model. In this study, a prediction method of output response probability for sound environment systems is derived by introducing a correction method based on the stochastic regression and fuzzy inference for simplified standard system models. The proposed method is applied to the actual data in a sound environment system, and the practical usefulness is verified.
Similar content being viewed by others
References
Franses P H (1998) Time series models for business and economic forecasting. Cambridge: Cambridge University Press
Han J, Lai T L, Spivakovsky V (2006) Approximate policy optimization and adaptive control in regression models. Computational Economics 27(4): 433–452
Lomadze V (2009) ARMA models and their equivalences. International Journal of Control 82(11): 2034–2039
Ikuta A, Ohta M, Siddique N H (2005) Prediction of probability distribution for the psychological evaluation of noise in the environment based on fuzzy theory. International Journal of Acoustics and Vibration 10(3): 107–114
Ikuta A, Masuike H, Ohta M (2005) A digital filter for stochastic systems with unknown structure and its application to psychological evaluation of sound environment. IEICE Transactions on Information and Systems E88-D(7): 1519–1522
Ikuta A, Orimoto H (2010) Prediction of output response probability for sound environment system by introducing stochastic regression and fuzzy inference for simplified standard system model. Proc. 9th IEEE International Conference on Cybernetic Intelligent Systems, Reading: 8–13
Lai T L, Ying Z (2006) Efficient recursive estimation and adaptive control in stochastic regression and ARMAX models. Statistica Sinica 16: 741–772
Takagi T, Sugeno M (1985) Fuzzy identification of systems and its application to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics 15(1): 116–132
Liu Z, Li H X (2005) A probabilistic fuzzy logic system for modeling and control. IEEE Transactions on Fuzzy Systems 13(6): 848–859
Ohta M, Koizumu T (1968) General statistical treatment of the response of a nonlinear rectifying device to a stationary random input. IEEE Transactions on Information Theory IT-14(4): 595–598
Lai T L (2003) Stochastic approximation. The Annals of Statistics 31: 391–406
Ikuta A, Orimoto H (2011) Adaptive noise suppression algorithm for speech signal based on stochastic system theory. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E94-A(8): 1618–1627
Orimoto H, Ikuta A (2012) A state estimation method for sound environment system with unknown observation mechanism by introducing fuzzy inference. Intelligent Information Management 4: 111–122
Author information
Authors and Affiliations
Corresponding authors
About this article
Cite this article
Ikuta, A., Siddique, N.H. & Orimoto, H. Prediction of output response probability of sound environment system using simplified model with stochastic regression and fuzzy inference. Fuzzy Inf. Eng. 5, 173–190 (2013). https://doi.org/10.1007/s12543-013-0142-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12543-013-0142-4