Joint proper orthogonal decomposition: A novel perspective for feature extraction from multivariate cavitation flow fields

Principal Orthogonal Decomposition (POD), as a data-driven method for extracting key features from fluid flow, overlooks the potential interactions and correlations among variables. This limitation restricts its effectiveness in capturing the underlying physical characteristics of the system. In this paper, we draw inspiration from the concept of joint representation in the field of multi-modal learning, and propose the use of Joint POD (JPOD) as a promising fluid mechanics analysis tool to extract multi-variable features of cavitation flow. We elaborate on the differences between JPOD and POD in four aspects: reconstruction error, data structure, flow field features, and flow modalities. JPOD increases the reconstruction error slightly but strengthens the correlations between multivariables in the flow field. The modalities obtained by JPOD exhibit strong regularity and interpretability, and the pattern features between different variables are related, which cannot be achieved by the POD algorithm alone. The successful combination of joint representation and POD algorithm demonstrates that it can be regarded as an optimization and standardization method for traditional modal decomposition algorithms, with broad application prospects in the field of modal decomposition.