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.

中文翻译：

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冶金数字孪生的自主残余监测


最近，工业应用的调查结果揭示了数字孪生维护的重要性。实际物理系统的变化会影响数字孪生和物理孪生之间的相似性，这可以从模型残差的不断变化中看出。在本研究中，提出了一种自主更新自我的方法，用于监测多变量残差。它独立于所使用的模型，并根据平方马氏距离监控归一化残差。主要的新颖性来自标准化，这是通过使用自动更新的最近残差的平均值和标准差值来完成的。通过使用磷酸盐选矿厂磨矿回路的离线仿真模型和金矿浮选回路的在线自适应数字孪生模型对该方法进行了研究。其性能与传统的平方马氏距离和主成分分析方法进行了比较。所提出的方法检测到异常的残差偏差，并且对初始训练数据特征的依赖性较低，由平均值和标准差定义。使用不同的数据集进行训练后，平方马氏距离的中位监测值始终保持在对应于 50-57% 卡方分布概率的值，而在没有自主更新的情况下，相应的值在 3-55% 和 39-88% 的范围内，由于训练数据集的分布不同，表现出不一致的性能。所提出的具有可转移和自配置属性的方法可以推进数字孪生的在线性能监测。