Time series analysis and prediction on complex dynamical behavior observed in 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 features of the data are investigated with diagnostic algorithm for instability and 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 measurement 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 similar to self-affine random noise. Characteristic exponents are estimated from the scaling properties of the prediction error as a function of the prediction-time interval. Such information is exploited as prior knowledge for designing a generalized Gaussian radial basis function network as a predictor. The performance of the network is improved when linear algebraic polynomials are added to the network. The characteristic exponents estimated are used as reliability indices of forecasting future trends of the data.