Improved multivariate sensor delay estimation using a hierarchical clustering-based approach

An often overlooked challenge in multivariate statistical modelling of industrial data is the presence of time delays caused by the residence time in the process, leading to event misalignment. To perform accurate data analysis, time delays must be estimated and corrected using a dedicated preprocessing step. Despite the multivariate nature of process data, most existing statistical Time Delay Estimation (TDE) methods only consider bivariate correlations. This study hypothesized that multivariate TDE methods would outperform bivariate methods, particularly with a large number of sensors. To test this, we selected data subsets with varying numbers of sensors using correlation-based hierarchical clustering and applied different TDE methods. Results showed that two multivariate methods, PLS-CON-LOAD and PLS-SEQ, outperformed the bivariate methods, exhibiting lower errors in the time delay estimation and less sensitivity to the number of sensors. Additionally, we proposed an enhancement to the TDE methods by embedding a clustering step to determine the order in which time delays should be estimated. This approach reduced TDE errors for all methods when number of sensors is high. We recommend the newly proposed clustering-based PLS-CON-LOAD method for low-error time delay estimation, which enhances the predictive value and insights obtainable from industrial data analysis.