Beware of r² even for test datasets: Using the latest measured y‐values (r²LM) in time series data analysis

The determination coefficient of a test dataset, r 2 , is calculated and used to compare the performance of adaptive soft sensors and discuss the possibility of their practical use. However, soft sensors that give very high r 2 values do not always have sufficient predictive accuracy for use in process control. Therefore, a new measure for soft sensors based on the latest measured y‐values (r 2 LM ) is proposed. This metric can be used in time series data analysis to determine whether the variations in y‐values estimated by soft sensors come from variations in the input variables or those of the latest measured y‐values. Through case studies using real and simulated datasets, it is confirmed that low r 2 LM values correspond to meaningless soft sensors, even when their r 2 value is high, and that high r 2 LM values imply that the estimation results are useful for process control with soft sensors. Python and MATLAB codes for computing r 2 LM can be downloaded from GitHub: https://github.com/hkaneko1985/r2lm .