Experiment-Validated Multiphysics Modeling, Generalizable Deep Learning and Interpretable Global Sensitivity Analyses for Thermoelectric Generators

Abstract

Thermoelectric generator (TEG) is a class of solid-state heat engine that directly converts heat into electricity. Despite extensive studies on the core thermoelectric materials, the inverse design of TEG operating conditions to harness their full potentials, remains challenging due to the high-dimensional design space. Recent efforts in deep learning of TEGs using artificial neural network (ANN) lack global sensitivity analyses and interpretation of the connection-weights, which leads to coupling effects unknown between input parameters and errors in importance ranking. To solve the above problems, a multiphysics 3D TEG model is established using the finite element method (FEM). The multiphysics simulation results are well validated by our experimental measurements of a TEG chip using self-built TEG performance evaluation system. A new 1D analytical TEG model under complex boundary conditions is developed for the first time, and proven consistent with the 3D FEM model. Interestingly, the inherent Peltier heat flux to the hot side, due to the Seebeck voltage, reduces the hot side temperature as the current becomes larger, indicating that the conventional iso-thermal boundary condition is not accurate at the device level. Then an ANN-based TEG model is trained, validated, and tested using the 3D TEG FEM results for the sensitivity analyses of key device operating parameters, 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 (Kc), and thermal contact resistance (Rc), with respect to the energy conversion efficiency (η). It is found that enhancing qh or hf guarantees the temperature difference for higher η. The variance-based GSA ranks the importance as qh>hf>RL>Ta≈Rc≈Kc, and reflects the coupling between qh and hf. The ANN model is generalizable towards larger ranges of these operating conditions. Finally, the neural interpretation diagram (NID) method shows that hf, qh and RL have a greater influence on η. NID also reflects the coupling effect between qh and hf through the contrast input-hidden connection weights of the same hidden node. This work provides a deep learning framework for TEGs using generalizable ANN and interpretable global sensitivity analyses, enabling the inverse design of practical TEG operating conditions towards higher energy conversion efficiencies.

Keywords: Thermoelectric Generator, Artificial Neural Network, Multiphysics modeling, finite element method, Sensitivity Analysis, Neural Interpretation Diagram