Local models for soft-sensors in a rougher flotation bank

Abstract Starting from a general approach for dynamic modelling, several classes of local dynamic models for soft-sensors are used to model the concentrate grade in a rougher flotation bank. Among the non-linear––but linear in the parameter––models are non-linear ARMAX, Takagi and Sugeno, fuzzy combinational, projection on latent states (PLS) and wavelet based models. The fully non-linear dynamic model studied is a multilayer perceptron. The models are identified using actual rougher plant data. This data––which is very noisy––is first analysed in order to detect apparent sporadic short term failures of the sensor system for measuring the concentrate grade and then to repair the failed measurements. The models are determined using an identification (training) data set. The root mean square error and the correlation coefficient are used to compare model performances using validation and cross validation data sets. Results show that the best dynamic models is PLS, followed by perceptron and wavelet based models. Non-linear ARMAX, fuzzy combination and Takagi and Sugeno dynamic models give somewhat larger errors.

[1]  G.D. Gonzalez,et al.  Soft sensors for processing plants , 1999, Proceedings of the Second International Conference on Intelligent Processing and Manufacturing of Materials. IPMM'99 (Cat. No.99EX296).

[2]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[3]  Timo Lättilä,et al.  An intelligent methodology for computer aided process study at mineral processing plants , 1995 .

[4]  Lennart Ljung,et al.  Nonlinear black-box modeling in system identification: a unified overview , 1995, Autom..

[5]  M. Hou,et al.  Multivariate statistical analysis of mineral processing plant data , 1993 .

[6]  Heinz Unbehauen,et al.  Fault Detection and Diagnosis with the Help of Fuzzy-Logic and with Application to a Laboratory Turbogenerator , 1996 .

[7]  Ana Casali,et al.  Dynamic simulator of a rougher flotation circuit for a copper sulphide ore , 2002 .

[8]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[9]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[10]  David L. Elliott,et al.  Neural Systems for Control , 1997 .

[11]  Heinz Unbehauen,et al.  Structure identification of nonlinear dynamic systems - A survey on input/output approaches , 1990, Autom..

[12]  Ana Casali,et al.  Particle size distribution soft-sensor for a grinding circuit , 1998 .

[13]  C. Burrus,et al.  Introduction to Wavelets and Wavelet Transforms: A Primer , 1997 .

[14]  S.Joe Qin,et al.  Neural Networks for Intelligent Sensors and Control — Practical Issues and Some Solutions , 1997 .