Data-driven temperature estimation of non-contact solids using deep-learning reduced-order models

A data-driven deep-learning reduced-order models (DL-ROMs) framework to accurately evaluate the temperature field of non-contact solids without available sensors is proposed in this paper. The framework combines a neural network (NN) and model reduction. The NN is trained and the sub-ROMs of internal non-contact solids are established based on a shared sample library in the offline stage. Specifically, proper orthogonal decomposition (POD) is used for data compression and feature extraction for a high-fidelity physical solution of the sample library, and then a lower-dimension approximation system is constructed on the projection space spanned by a set of reduced orthogonal basis. An NN is introduced to implicitly map inlet conditions or temperature data measured by external sensors to the feature coefficients of the established sub-ROMs regardless of the complex flow heat transfer mechanism. Prediction under a new inlet condition or monitoring based on measured temperatures can be conducted using this framework in the online stage. Six groups testing in-sample and out-of-sample cases are used to verify the feasibility and robustness of the framework. The results show that the proposed framework can effectively predict and monitor the temperature field of internal non-contact solids for in-sample cases. The framework is also suitable for extrapolation cases that exceed 10% of the sample range. This framework is used to estimate the temperature field of non-contact solids in complex industrial problems to further develop parametric design, real-time prediction, optimal control strategies, and online monitoring and maintenance.