Abstract In turbomachinery design, the accurate prediction of the life cycle is one of the most challenging issues. With increasing thermal loads, thermomechanical fatigue in the turbine has become a focal point of increasing attention. To incorporate thermally induced stress in the turbine as a part of high pressure turbine heat transfer design, the primary requirement is to predict blade metal temperature accurately. However, current high-temperature measurement technology can only measure the surface temperature or the limited discrete points temperature of the turbine blade and fails to capture the temperature field of the entire metal. Traditionally, turbine designers use numerical simulation to supplement these thermal details; however, the unknown boundary conditions of the solid domain and complicated flow field lead to a lack of fidelity or economic viability in the results. Therefore, the industry has been continuously seeking mathematical tools to address this problem. The present study proposed a deep learning method based on a physics-encoded neural network. The proposed method can invert the transient temperature field of the metal during the whole steady flow cycle using limited surface temperature time-series data. This implies that just a few seconds of data is sufficient to obtain the temperature field for tens of minutes or even hours, significantly reducing experiment costs. The detailed discussion on the theory of the deep learning method is followed by three aspects of testing to verify the application and accuracy of the proposed method.
Hao et al. (2025) studied this question.