Spectral partial least square based mode decomposition: an extension of SPOD incorporating two datasets

This work introduces a Spectral Partial Least Squares (SPLS)-based mode decomposition method, designed as an extension of Spectral Proper Orthogonal Decomposition (SPOD). In contrast to traditional modal analysis approaches, SPLS levarages two input datasets, such as high-dimensional time-series flow field data and low-dimensional time-varying signals acquired from microphones. SPLS extracts modes that maximize the covariance of their projections. A space-time inner product formulation, analogous to SPOD, is employed to extract frequency-specific modes that incorporate information from both datasets. The resulting energetic SPLS modes reflect strong correlations between the two datasets at each frequency. We demonstrate the proposed method using an open-source subsonic turbulent jet dataset by large-eddy simulation. In this case, while SPOD and SPLS both utilize the full jet flow field, SPLS uniquely incorporates data from a localized region associated with upstream-propagating acoustic waves within the jet potential core. This enables SPLS to identify dominant modes influenced by the localized input region. The extracted SPLS modes reveal upstream-propagating acoustic waves that are less clearly identified by SPOD. These results highlight the capability of SPLS to extract energetically significant modes that represent strong correlations between disparate datasets, such as the combination of sparse measurements and full-field flow data.