Visualization of the controller states of an autogenous mill from time series data

The operational variables of an industrial autogenous mill were embedded in a low-dimensional phase space to facilitate visualization of the dynamic behavior of the mill. This was accomplished by use of a multivariate extension of the method of delay coordinates used in nonlinear time series analysis. In this phase space, the controlled states of the mill could be visualized as separate regions or clusters in the phase space. Comparison of the correlation dimension of the state variable of the mill (the load) embedded in phase space suggested that the dynamic behavior of the mill could not be represented by a linear stochastic model (Gaussian or otherwise). The low dimensionality (≤2) of the correlation dimension further suggested that the mill load depended on a few variables only and that the underlying generative process had a significant deterministic component. In addition, the operational variables could be used as reliable predictors in a neural network model to identify the controlled states of the mill. As a complementary approach to visualization of the operation of the mill, a different neural network model could be used to reconstruct a corrected power load curve by compensating for the effect of varying operating conditions