Time series analysis and prediction on complex dynamical behavior observedin a blast furnace

This paper describes a strategy for building a predictive model for actual complex time series. Time series data of temperature fluctuations observed in a blast furnace for iron-making are taken as an example. Chaotic feature s of the data are investigated with diagnostic algorithm for instability an d parallelism of neighboring trajectories in phase space reconstructed from the time series data. Stationarity of the data is examined with diagnostic algorithm based on the KM2O-Langevin equations developed by Okabe. A short time series for which no control actions were taken to the plant during me asurement is diagnosed as possibly low-dimensional chaos, while for a long time series including many control actions during measurement, determinism is less visible and its predicted behavior exhibits a scaling property simi lar to self-affine random noise. Characteristic exponents are estimated fro m the scaling properties of the prediction error as a function of the predi ction-time interval. Such information is exploited as prior knowledge for d esigning a generalized Gaussian radial basis function network as a predicto r The performance of the network is improved when linear algebraic polynomi als are added to the network. The characteristic exponents estimated are us ed as reliability indices of forecasting future trends of the data. (C)2000 Elsevier Science B.V. All rights reserved.