Flow reconstruction from sparse sensors based on reduced-order autoencoder state estimation

The reconstruction of accurate and robust unsteady flow fields from sparse and noisy data in real-life engineering tasks is challenging, particularly when sensors are randomly placed. To address this challenge, a novel Autoencoder State Estimation (AE-SE) framework is introduced in this paper. The framework integrates sensor measurements into a machine learning-based reduced-order model (ROM) by leveraging the low-dimensional representation of flow fields. The proposed approach is tested on two direct numerical simulation benchmark examples, namely, circular and square cylinders and wake flow fields at Re = 100. The results demonstrate satisfactory performance in terms of accuracy and reconstruction efficiency. It achieves the same accuracy as traditional methods while improving reconstruction efficiency by 70%. Moreover, it preserves essential physical properties and flow characteristics even in the noisy data, indicating its practical applicability and robustness. Experimental data validation confirms a relative error below 5% even at a noise level of 12%. The flexibility of the model is further evaluated by testing it with a trained ROM under varying Reynolds numbers and benchmark cases, demonstrating its ability to accurately estimate and recognize previously unseen flow fields with appropriate training datasets. Overall, the proposed AE-SE flow reconstruction method efficiently and flexibly leverages ROM for the low-dimensional representation of complex flow fields from sparse measurements. This approach contributes significantly to the development of downstream applications such as design optimization and optimal control.