Abstract

State estimation in complex processes such as the semi-autogenous grinding process (SAG) in copper mining is an important and difficult task due to difficulties for real-time and on-line measuring of some relevant process variables. This paper extends a comparison, initiated in previous work of the same authors, between NARX and NARMAX dynamic models built using Artificial Neural Networks (ANN) and Support Vector Machines (SVM), when acting as estimators of one of the most important state variables for SAG milling operation. To accomplish this comparison we propose a simple and original methodology to develop NARMAX models with SVM. The results show that SVM-NARMAX models outperform SVM-NARX models because they incorporate previous prediction errors in order to improve prediction of the future evolution of the process. Advantages of SVM over those RNA models are also highlighted. NARMAX-SVM has a significantly lower MSE than all other models. In terms of the milling process, it provides a useful tool for estimating important state variables that are not easily available on-line and in real time thus aiding control and monitoring of the process.