Radiative properties estimation with the Particle Collision Algorithm based on a sensitivity analysis
Diego C. Knupp, Antônio J. Silva Neto and Wagner F. Sacco
Implicit formulations for parameter estimation inverse problems in which a cost function is minimized have largely been employed in several applications related to heat and mass transfer. Even though gradient based methods have been used in most cases, it has been observed an increasing interest in the use of stochastic methods for the solution of inverse radiative transfer problems. A hybrid approach with the Particle Collision Algorithm (PCA) – a recently developed stochastic method – and the Levenberg-Marquardt (LM) – a deterministic method – has been successfully used by the authors for the solution of the inverse problem of participating media radiative properties estimation. In such approach it is required the solution of the direct radiative transfer problem which is modeled by the linear version of the Boltzmann equation. For that purpose it is used a discrete ordinates method combined with the finite difference method. Even though good results have been obtained, it has been observed that the PCA solution, which is later used as the initial guess for the LM, shows lower quality when experimental data with low sensitivity to the parameters we want to estimate are used. Here we identify and use for the solution of the inverse problem only the data with higher sensitivity. This approach yields better results and prevents LM from not converging.
Keywords: Levenberg-Marquardt, Particle Collision Algorithm, radiative transfer, sensitivity analysis, inverse problem, optimization, stochastic method.