Experiment-Validated multiphysics modeling, generalizable deep learning and interpretable global sensitivity analyses for thermoelectric generators

Despite extensive studies on thermoelectric materials in a thermoelectric generator (TEG), the inverse design of TEG operating conditions remains challenging. Recent efforts in deep learning of TEGs using artificial neural network (ANN) lack global sensitivity analyses and interpretation of the connection-weights, leading to unknown coupling between input parameters and errors in importance ranking. This work reports a deep learning framework for TEGs using generalizable ANN, interpretable local (LSA) and global sensitivity analyses (GSA). Sensitivity analyses are applied to determine how energy conversion efficiency (η) under the practical Neumann and Robin thermal boundary conditions is affected by TEG operating conditions, including hot-side heat flux (qh), cold-side convective heat transfer coefficient (hf), temperature of the cooling medium (Ta), load resistance (RL), electric contact resistance (Rc), and thermal contact resistance (Kc). First, multiphysics TEG simulation results based on 3D finite element method (FEM) are validated by our experimental measurements using a self-built TEG performance evaluation system. The partial derivative-based LSA is done on a 1D theoretical TEG model to obtain the trend in sensitivity factors. Then, an ANN model is trained and validated based on the FEM simulation results and applied to the GSA process, aiming at reducing the computational load. Variance-based GSA is applied on the ANN model to determine the importance ranking and reflect the coupling between input parameters. The variance-based GSA ranks the importance as qh>hf>RL>Ta≈Rc≈Kc, and reflects the coupling between qh and hf. Finally, to interpret the ANN and the hidden deep learning process, a method combining the connection-weights algorithm and neural interpretation diagram (NID) is proposed to extract the hidden information in the connection weights. The ANN model is proven generalizable towards larger ranges of operating conditions. This work provides a framework to design TEG operating conditions towards higher energy conversion efficiencies.