Inverse Problem Regularization of Parametric Identification of the Particle Temperature Distribution of Gas-Thermal Flow with Optimization of Its Solution

Abstract

AbstractThe inverse problem of parametric identification of the model function of the temperature distribution density of heterogeneous flow particles, which form functional powder coatings on the surface of technical products in the process of their thermal spraying, is considered. The regularization of this ill-posed inverse problem consists in choosing a physically adequate parameterized model function of the density of the particle temperature distribution using the registered spectrum of the particle thermal radiation. Structural diagrams of the complex for recording the spectrum of particle thermal radiation and the complex for its calibration are given. As the objective function of parametric optimization, the criterion function of the least squares method (LSM) is used. This function is defined as the sum of the squared deviations of the experimental readings of the thermal radiation spectrum of particles from the calculated values of its model spectrum corresponding to these readings. The model spectrum of the thermal radiation of particles is determined by the integral Fredholm operator of the first kind with the kernel of the operator based on the Planck function and the model parametrized function of the density of the particle temperature distribution. The Planck function depends on the temperature and wavelength of the thermal radiation of particles. Computational experiments were carried out to analyze the accuracy and numerical stability of the parameters being optimized when solving the inverse problem. The influence of the error aperture in the registered spectrum of the thermal radiation of particles on the estimate of the “shift” of the optimized parameters of the model density function of the particle temperature distribution is studied. Numerical modeling and experimental verification have shown that the accuracy and numerical stability of the regularized solution to measurement errors of the recorded spectrum of particle thermal radiation can be improved. KeywordsRegularizationInverse problemParametric identificationParticle temperature distributionFredholm integral operator of the 1st kindThermal radiation spectrumGas-thermal flowCoating