Nonlinear Modeling Method Applied to Prediction of Hot Metal Silicon in the Ironmaking Blast Furnace

Abstract

Feedforward neural networks have been established as versatile tools for nonlinear black-box modeling, but in many data-mining tasks the choice of relevant inputs and network complexity still constitute major challenges. Statistical tests for detecting relations between inputs and outputs proposed in the literature are largely based on the theory for linear systems, and laborious retraining combined with the risk of getting stuck in local minima make the application of exhaustive search through all possible network configurations impossible but for toy problems. This paper proposes a systematic method to tackle the problem where an output shall be estimated on the basis of a (large) set of potential inputs. Feedforward neural networks of multilayer perceptron type are used in the three-stage approach: First, starting from sufficiently large networks, an efficient pruning method is applied to detect potential model candidates. Next, the best results of the pruning runs are extracted by forming a Pareto-frontier, with the contradictory objectives of minimizing network complexity and estimation error. The networks on this frontier are considered to contain promising hidden nodes with their specific connections to relevant input variables. These hidden nodes are therefore optimally combined by mixed-integer linear programming to form a final set of neural network models, from which the user can select a model of suitable complexity. The modeling method is applied on an illustrative test example as well as on a complex modeling problem in the metallurgical industry, i.e., prediction of the silicon content of hot metal produced in a blast furnace. It is demonstrated to find relevant inputs and to yield parsimonious sparsely connected neural models of the output.

Adaptive Weighting Just-in-Time-Learning Quality Prediction Model for an Industrial Blast Furnace

“…Two following weighting strategies are considered for the variables in the projected space: (1) (12); (2) eigenvalue based weighting, with its weights assigned as Eqs. (12) and (13).…”

“…To online predict the silicon content, various data-driven soft sensor modeling approaches, including various neural networks, [7][8][9][10][11][12][13][14] partial least squares, 14,15) fuzzy inference systems, 16) nonlinear time series analysis, [17][18][19][20] subspace identification, 21) support vector regression (SVR) and least squares SVR (LSSVR), [22][23][24] and others [25][26][27][28][29] have been investigated. A recent overview of black-box models for short-term silicon content prediction in blast furnaces can be referred to.…”

Blast Furnace Dynamics Using Multiple Autoregressive Models with Exogenous Inputs

“…Table 1: These variables include information about the combustion (blast volume and oxygen content, specific coke and coal consumption), heat level (tuyere energy and heat losses), gas permeability (blast pressure and gas resistance) and gas utilization (top gas CO utilization and CO+CO2 content), which are all known to either affect or reflect the hot metal silicon content. A more detailed analysis of the variables is presented in Nurkkala et al 20) In addition, the autoregressive part of the model includes old observations of the silicon content, Si. …”

“…17) Techniques based on evolving or pruning neural networks have also been proposed. [18][19][20] However, the problem of fundamentally changing dynamics has not been adequately tackled: To the best of the authors' knowledge, except for some preliminary trials 21) switching between multiple models has not been elaborated for the hot metal silicon prediction problem. This is somewhat surprising as the complexity of the system and the possibility of multiple stable states mentioned above would speak for such an approach.…”

“…This is somewhat surprising as the complexity of the system and the possibility of multiple stable states mentioned above would speak for such an approach. In the present paper, a simple multiple-model strategy is devel-© 2012 ISIJ oped, partly using findings from earlier studies of a data set 20) and partly on the basis of the characteristics of the data set. For the data periods of the "training set", a set of linear ARX models is developed, and for the future data a selection among these models for prediction is proposed based on their performance on the recent past.…”