Model-free real-time MRT temperature inversion: hybrid adaptive differential evolution with local refinement

Multispectral Radiation Thermometry (MRT) enables precise non-contact temperature measurement, critical for aerospace thermal protection systems and metal heat treatment monitoring. The underdetermined radiative transfer equation complicates temperature-emissivity decoupling, with traditional methods relying on a priori emissivity assumptions, often leading to systematic errors. To address these limitations, this study proposes a hybrid adaptive differential evolution algorithm with local refinement (HADE-LR), supported by a reference-temperature model that stabilizes the inversion process. Key innovations include: (1) Latin hypercube sampling for initial population construction to optimize parameter space exploration; (2) an adaptive variational-crossover operator to enhance global search efficiency; and (3) a three-stage local optimizer combining Nelder-Mead simplex, L-BFGS-B quasi-Newton, and damped Newton methods for high-precision solutions. Numerical simulations across six emissivity models achieved a maximum temperature relative error of 0.4513% at 1800 K. Validation on silicon carbide and alloy steel further shows inversion errors below 0.44% under noise levels up to 5%, with emissivity curves closely matching measurements. The algorithm operates without emissivity-model assumptions, supports extended emissivity bounds, and achieves real-time performance with an average computation time of 0.14 s. These results highlight the robustness, efficiency, and broad applicability of HADE-LR for high-temperature MRT. Graphical figure. Flowchart of the HADE-LR algorithm