Evolving nonlinear time-series models of the hot metal silicon content in the blast furnace

Neural networks are versatile tools for nonlinear modeling, but in time-series modeling of complex industrial processes the choice of relevant inputs and time lags can be a major problem. A novel method for the simultaneous detection of relevant inputs and an appropriate structure of the lower part of the networks has been developed by evolving neural networks by a genetic algorithm, where the approximation error and the number of weights are minimized simultaneously by multiobjective optimization. The networks on the Pareto front are considered possible candidate models that are evaluated on an independent test set. In order to consider the problem of drift in the variables, which may cause parsimonious models to perform poorly on the test set, the weights in the upper layer of the networks are recursively estimated by a Kalman filter. The method is illustrated on a data set from ironmaking industry, where time-series models of the hot metal silicon content in a blast furnace are evolved. The technique is demonstrated to synthesize models with a choice of inputs in agreement with findings presented in the literature and process know-how.