Evolving Nonlinear Time-Series Models of the Hot Metal Silicon Content in the Blast Furnace

Abstract

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.

Nonlinear Prediction of the Hot Metal Silicon Content in the Blast Furnace

“…21,22) In most of these efforts, the input variables in the models have been selected on the basis of process knowledge, but in some of the papers more systematic approaches have been made. For instance, Waller and Saxén 12) applied an exhaustive search among linear finite impulse response (FIR) models using a large set of inputs with different time lags, Bhattacharya 20) used a partial least squares procedure to select relevant inputs, while Saxén et al 23) evolved sparsely connected neural network models of the silicon content by a genetic algorithm. However, in practically all approaches on nonlinear prediction of the silicon content by neural networks, a small set of potential inputs was always selected a priori.…”

“…Even though the main mechanisms behind the silicon transfer have been clarified, i.e., the gasification of SiO 2 from coke and coal ash to SiO(g) in the high temperature region at the tuyere level, and its reduction to silicon in the liquid iron, the most successful approaches to short-term prediction (e.g., on a tap to tap basis) of the hot metal silicon content are based on stochastic models because of uncertainty in the estimates of the internal state and dynamics of the high-temperature region. Numerous black-box models for the prediction of the hot metal silicon content have been developed, [8][9][10][11][12][15][16][17][18][19][20][21][22][23] and some recent papers have stressed the chaotic nature of the signal. 21,22) In most of these efforts, the input variables in the models have been selected on the basis of process knowledge, but in some of the papers more systematic approaches have been made.…”

Real-World Applications of Multiobjective Optimization

“…Very recently this methodology has been augmented further through the use of Kalman filters (Saxén et al, 2007), and it has also been effectively utilized for identifying the most important in-signal in a very large network (Pettersson et al, 2007b), rendering it of further interest to the soft computing researchers at large. (Pettersson et al, 2007a).…”

Combined control of aluminum bath composition by X‐ray diffraction and X‐ray fluorescence analysis

“…[26] In engineering and industry, GAs are used for a dynamic optimization of an industrial polymerization reactors, [27] continuous steel casting, [28,29] prediction of silicon content in the hot metal during ironmaking process [30] and oil stabilization. [31] Genetic algorithms are also used in diffraction structural analysis [32,33] to determine the approximate models of crystal structures of materials.…”