Hybrid first‐principles/neural networks model for column flotation

A new model for phosphate column flotation is presented which for the first time relates the effects of operating variables such as frother concentration on column performance. This is a hybrid model that combines a first-principles model with artificial neural networks. The first-principles model is obtained from material balances on both phosphate particles and gangue (undesired material containing mostly silica). First-order rates of net attachment are assumed for both. Artificial neural networks relate the attachment rate constants to the operating variables. Experiments were conducted in a 6-in.-dia. (152-mm-dia.) laboratory column to provide data for neural network training and model validation. The model successfully predicts the effects of frother concentration, particle size, air flow rate and bubble diameter on grade and recovery.

[1]  James A. Finch,et al.  Bubble size estimation in a bubble swarm , 1988 .

[2]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[3]  Elijah Polak,et al.  Computational methods in optimization , 1971 .

[4]  Enrique Luis Lima,et al.  Hybrid-neural modeling for particulate solid drying processes , 1996 .

[5]  James A. Finch,et al.  Mixing Characteristics of industrial flotation columns , 1985 .

[6]  James L. McClelland,et al.  Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations , 1986 .

[7]  Timothy Masters,et al.  Practical neural network recipes in C , 1993 .

[8]  Gerald H. Luttrell,et al.  A flotation column simulator based on hydrodynamic principles , 1991 .

[9]  Steven C. Chapra,et al.  Numerical Methods for Engineers , 1986 .

[10]  Paul Mavros.  Mixing in flotation columns. Part I: Axial dispersion modelling , 1993 .

[11]  Francisco A. Cubillos,et al.  Identification and optimizing control of a rougher flotation circuit using an adaptable hybrid-neural model , 1997 .

[12]  Markus A. Reuter,et al.  A generalized neural-net kinetic rate equation , 1993 .

[13]  Mark A. Kramer,et al.  Modeling chemical processes using prior knowledge and neural networks , 1994 .

[14]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[15]  James A. Finch,et al.  Column flotation: A selected review, part II , 1991 .

[16]  James A. Finch,et al.  The axial dispersion model in flotation column studies , 1991 .

[17]  Lyle H. Ungar,et al.  A hybrid neural network‐first principles approach to process modeling , 1992 .