Comparison of surrogate models used for adaptive optimal control of active thermoelectric windows

This paper compares the performances of standard surrogate models in the development of an optimal control framework. The optimal control strategy is implemented on an Active Thermoelectric (ATE) window design. The ATE window design uses thermoelectric units to actively regulate the overall thermodynamic properties of the windows. The optimization of the design is a multiobjective problem, where both the heat transferred through the window and electric power consumption are minimized. The power supplies and the heat transfer are optimized under a reasonable number of randomly sampled environmental conditions. The subsequent optimal designs obtained are represented as functions of the corresponding environmental conditions using surrogate models. To this end, four types of surrogate models are used, namely, (i) Quadratic Response Surface Methodology (QRSM), (ii) Radial Basis Functions (RBF), (iii) Extended Radial Basis Functions (E-RBF), and (iv) Kriging. Their performances are compared using two accuracy measurement metrics: Root Mean Squared Error (RMSE) and Maximum Absolute Error (MAE). We found that any one of the surrogate modeling methods is not superior to the others over the whole domain for the optimal control of the ATE window.