Autonomous residual monitoring of metallurgical digital twins

The importance of digital twin maintenance has recently surfaced through findings from industrial applications. Changes in actual physical systems affect the resemblance between digital and physical twins, which can be seen in the continuously changing variation in model residuals. In this study, a method that autonomously updates itself is proposed for monitoring multivariate residuals. It is independent of the models used and monitors normalised residuals based on the squared Mahalanobis distance. The main novelty comes from the normalisation, which is done by using autonomously updated mean and standard deviation values of recent residuals. The method was studied by using an offline simulation model of a grinding circuit in a phosphate concentrator and an online adaptive digital twin model of a flotation circuit in a gold mine. Its performance was compared with conventional squared Mahalanobis distance and principal component analysis methods. The proposed method detected abnormal residual deviations and had low dependence on the characteristics of initial training data, defined by mean and standard deviation. After training with different data sets, the median monitored values of squared Mahalanobis distance remained consistently at values corresponding to 50–57% chi-square distribution probabilities, whereas without autonomous updating, the corresponding values were in the ranges of 3–55% and 39–88% showing inconsistent performance due to the varying distributions of training data sets. The proposed method with transferable and self-configuring properties can advance the online performance monitoring of digital twins.