Diagnosis of oscillations in an industrial mineral process using transfer entropy and nonlinearity index

Abstract

Oscillations in mineral processes can propagate through multiple units, causing important controlled variables to deviate from their set points and degrade control performance. Root cause diagnosis of oscillations enables corrective action to return to desired operation. Numerous data-based methods for diagnosis of oscillations have been developed. Transfer entropy and the nonlinearity index are popular techniques that have been proven effective for oscillation diagnosis for a number of processes. Transfer entropy is a causality analysis technique. Causal relationships between measured variables are inferred, which allows the oscillation propagation path to be traced. The nonlinearity index ranks variables according to their nonlinearity content. The assumption is that the nonlinearity is greatest close to the oscillation source, since the process acts as a linear filter as the oscillation propagates.

An oscillation propagating through multiple control loops in a mineral processing plant was identified. The validity of transfer entropy and nonlinearity index for oscillation diagnosis was compared, highlighting their benefits and pitfalls when applied to a real industrial case study. The results revealed contradictory root causes for transfer entropy and the nonlinearity index. Consideration of process knowledge indicated that the transfer entropy results were consistent with the material flow and control structure. This indicates that transfer entropy accurately traced the oscillation propagation, while the nonlinearity index gave erroneous results. Nonlinear behaviour occurring in the process caused nonlinear trends to develop downstream of the root cause, making the assumptions of the nonlinearity index invalid. This result demonstrates the need for careful analysis of fault diagnosis results using expert knowledge of the process.