Interpreting complex flows, which may include transient features, non-linearity, and high dimensionality, is challenging because averages may not represent any individual flow field. This work evaluates the variability of dimensionally-reduced flow field data measured using Particle Image Velocimetry (PIV) compared to an ensemble mean, using several novel vector comparison metrics, namely; Weighted Relevance Index (WRI), Weighted Magnitude Index (WMI), and a modified Combined Magnitude and Relevance Index (modified-CMRI). Three dimensionality-reduction techniques were assessed, Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD) and Sparsity-Promoting DMD (SPDMD) using the proposed metrics. The PIV data were collected using an optically accessible single-cylinder engine under motored conditions at two crank-angle degrees (CAD), 460 CAD (maximum inlet valve lift) and 700 CAD (a typical spark-timing angle). The results show that the 0 Hz SPDMD mode preserves the vector magnitude and alignment and thereby better captures intake jet dynamics, aligning more closely with individual snapshots than ensemble averaging. Furthermore, the metrics consistently identify discrepant snapshots in both datasets when compared to the 0 Hz SPDMD mode, outperforming the traditional ensemble mean approach. These findings underscore the utility of the proposed vector comparison metrics in evaluating dimensionality reduction techniques and their potential to enhance the analysis of complex flow fields, ultimately aiding in the identification of cycle-to-cycle variations (CCVs) in large in-cylinder flow datasets. Taken together, the use of SPDMD to extract a physically representative reference flow field and the modified-CMRI to quantify deviations from individual cycles, provides a unified framework for analyzing in-cylinder highly variable flows.
Goswami et al. (2026) studied this question.