Adaptive restoration and reconstruction of incomplete flow fields based on unsupervised learning

Abstract

Due to experimental limitations and data transmission constraints, we often encounter situations where we can only obtain incomplete flow field data. However, even with incomplete data, we can still extract valuable information about the main structural characteristics of the flow field. In this study, we propose a novel unsupervised learning reconstruction method to restore the incomplete flow field data. Our method comprises several key steps: First, based on the temporal evolution characteristics of the flow field, we employ the Autoregressive Integrated Moving Average model method to pre-reconstruct the incomplete data. Next, we introduce the Fuzzy Spatial Consistency Index (FSCI), which measures the spatial coherence among neighboring data variations. By utilizing FSCI as a guiding metric, we iteratively optimize and replace missing values using the Proper Orthogonal Decomposition method. Importantly, our reconstruction process does not rely on expensive high-fidelity data fusion or external intervention, making it highly efficient and cost-effective. We focus our research on the classic problem of flow around the hydrofoil and apply the unsupervised learning reconstruction method to restore incomplete flow fields with varying missing rates. We also investigate the impact of flow field stability, snapshot sampling frequency, and missing structure on reconstruction accuracy. Our results indicate that these factors significantly influence the reconstruction of velocity fields with a high missing rate compared with a lower missing rate. Additionally, we observe that the reconstruction performance of the streamwise velocity field is relatively inferior compared to the normal velocity field, and the reconstruction accuracy is higher for relatively stable flow fields. These findings provide valuable insights and further validate the effectiveness and applicability of the unsupervised learning reconstruction method for restoring incomplete flow fields.