Rapid Online Estimation of Time-Varying Thermal Boundary Conditions in Convective Heat Transfer Problem by ANN-Based Extended Kalman Smoothing Algorithm

In modern technologies, such as digital twin, it is essential to make real-time estimations of unknown time-varying boundary conditions from sensor measured data in given thermal systems, which leads to inverse heat transfer problems (IHTPs). However, due to the complexity of IHTPs, it’s quite challenging to obtain a stabilized solution for online estimation with affordable computational cost. In this work, a rapid yet robust inversion algorithm called ANN-based extended Kalman smoothing algorithm is developed to realize the online estimation of unknown time-varying boundary conditions. Under the state-space representation of the extended Kalman smoothing algorithm, pre-trained fast ANN structures are deployed to replace the conventional CFD-based state transfer models, from which the computational process can be further accelerated by reducing the dimension of state variables. Two-dimensional tube convective heat transfer problem was employed as the case study to test the algorithm. The results show that the proposed algorithm is indeed a computational-light and anti-interference approach for solving IHTPs. The proposed algorithm can achieve estimation of unknown boundary conditions with a dimensionless average error of 0.0580 under noisy temperature measurement with a standard deviation of 10 K and its computational cost is reduced drastically compared with conventional approach from 12.23 s per time step to 3.506 ms.