Multispectral two-dimensional temperature field reconstruction using particle swarm optimization and the Broyden–Fletcher–Goldfarb–Shanno algorithm with multiple extreme value optimization

Abstract

The flame temperature is a crucial parameter in combustion, indicating heat generation and transfer. However, determining the correct temperature becomes challenging when flame emissivity is unknown. This article presents a multispectral 2D temperature field reconstruction method using particle swarm optimization and the Broyden–Fletcher–Goldfarb–Shanno algorithm, combined with multivariate extreme-value optimization. This method establishes an objective function based on the correlation between the true temperature and spectral data. The objective function was minimized by adjusting the emissivity, enabling the reconstruction of 2D temperature and emissivity images without assuming an emissivity model. Calibration with a multispectral camera yielded the spectral response coefficients, and three-time spline interpolation was used to verify the calibration data. The reconstructed 2D temperature field showed a mean absolute error (MAE) of 4.61 and structural similarity (SSIM) of 0.995. The reconstructed emissivity image had an MAE range of 0.04 to 0.053 and an SSIM range of 0.897 to 0.915. The system, tested on a butane flame, showed a temperature range of 1001 K to 1356 K, with an average temperature of 1194 K and emissivity values ranging from 0.3166 to 0.8621. The results align with the expected combustion process and radiation characteristics distribution of the butane flame.