Missing data treatment for locally weighted partial least square‐based modelling: A comparative study

Abstract

Adaptive soft sensors including widely used locally weighted partial least square (LW‐PLS) have been established for online prediction, fault detection, and process monitoring. Nevertheless, majority of these existing adaptive soft sensors have zero tolerance to missing data, and the presence of missing data is inevitable due to sensor failures, routine maintenance, changes in sensor equipment over time, merging data from different system, and so forth. In the literature, limited studies could be found on the effects of missing data and the existing missing data imputation methods on the predictive performances of adaptive soft sensors. This work reports combined use of different missing data imputation techniques on LW‐PLS and the nonadaptive soft sensor, the partial least square (PLS). Well known trimmed score regression (TSR) and singular value decomposition (SVD) were employed in this study, and thus, the newly integrated TSR‐LW‐PLS and SVD‐LW‐PLS algorithms were proposed. Meanwhile, both existing TSR‐PLS and SVD‐PLS were used, and their results compared with the novel TSR‐LW‐PLS and SVD‐LW‐PLS algorithms. These algorithms were tested and evaluated using two examples having different percentages of missing data ranging from 5% to 40%. Results showed that TSR‐LW‐PLS model was superior compared with SVD‐LW‐PLS, TSR‐PLS, and SVD‐PLS as indicated by more than 100% improvements in prediction accuracy. It was also evident that TSR‐LW‐PLS is able to cope well with up to 20% of missing data.

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“…R 2 is a statistical metric that determines how well actual and expected variables match up with one another. The formula in its entirety may be found in Equation (3) [ 24 ]. …”