Generalized inverse matrix-exterior penalty function (GIM-EPF) algorithm for data processing of multi-wavelength pyrometer (MWP)

The unknown emissivity of materials is a huge obstacle in multi-wavelength pyrometry (MWP). It leads to a set of ill-posed equations that cannot be directly inverted to obtain the true temperature from a set of multi-wavelength measurements. Constraint optimization algorithms such as the gradient projection (GP) and internal penalty function (IPF) algorithms provide solutions without any emissivity model assumptions but require a narrow fixed emissivity range and an appropriate initial emissivity input value, otherwise, accuracy and computational efficiency are greatly affected. Here, we propose a generalized inverse matrix-exterior penalty function (GIM-EPF) algorithm to realize an efficient and accurate inversion without limiting the emissivity range in advance. First, a set of emissivities is obtained by the generalized inverse matrix method; these emissivities are used as initial values in the exterior penalty function iteration algorithm, from which temperature and spectral emissivity are obtained. Simulation results show that the GIM-EPF algorithm provides results superior to IPF, especially in computational efficiency. The proposed GIM-EPF method is 8 times faster than the IPF method with a 0.56% relative error at the 1800 K true temperature. The GIM-EPF method also allows near real-time diagnosis of rocket exhaust flame temperature. Rocket nozzle temperature experiment results show that the temperatures derived by the GIM-EPF algorithm agree well with the theoretical design temperature and the IPF inversion temperature.