Experimentally constrained Gaussian-process modeling and multi-objective optimization of local brick-surface temperatures in a tunnel-kiln cooling zone

The cooling zone of a tunnel kiln removes heat from a densely packed brick load by forced convection, and its local performance depends on the brick arrangement, the guide vanes, and the airflow. Previous experimental campaigns examined these factors separately, and no unified predictive model links them to the local brick temperatures. This study combines 534 runs from two published campaigns on the same 1:4 scale cooling zone facility and relates six inputs, namely guide vane configuration, vane angle, brick setting, number of layers, the column spacing fixed by each setting (0.0193-0.058 m), and inlet velocity (2.38-6.45 m/s), to the surface temperatures of four electrically heated model bricks. Six regression methods were compared by repeated and grouped cross-validation, and the best surrogate was coupled with a constrained NSGA-II search restricted to experimentally tested combinations, with the spacing assigned from the setting. Gaussian process regression was the most accurate interpolator (mean R 2 = 0.989; RMSE 1.25-1.49 °C), but its mean R 2 fell to 0.689 when complete design cells were withheld, showing that the high random fold accuracy mainly reflects interpolation within already represented regions. The side wall guide vane lowered all four temperatures by 6.5-7.9 °C relative to the no-vane condition, whereas the vane angle changed them by about 2 °C, and the transversal near wall brick was the hottest position and the one least associated with the design factors. The surrogate-predicted best compromise within the tested bounds (side wall guide vane at 150°, brick setting 2, eight layers, 0.058 m spacing, and 6.45 m/s) yields 69.93, 86.28, 54.39, and 75.18 °C at the four positions, and the same design was selected in ten repeated optimization runs, in six algorithm variants, and under uncertainty-aware selection. Because its velocity lies at the upper bound of the tested range and beyond the velocities tested for its own design cell, it requires experimental confirmation. Moreover, pressure drop and fan power were not optimized, so the results reflect spatial cooling performance rather than a complete thermal energy trade-off. The framework offers a rapid, experimentally bounded tool for laboratory-scale design screening; using it for smart kiln control would first require validation on an industrial kiln.