Modeling of a thermal response of cast-iron concrete system under active thermal non-destructive testing

The article is devoted to mathematical modeling of the thermophysical experiment related to diagnostics of a space under a cast-iron tubbing of a shaft lining by the optical lock-in thermography. In the article it is presented a numerical solution of the twodimensional boundary value problem that describes heat transfer processes by conduction, convection and radiation. Detection of a defect placed within the space under the tubbing is carried out by analyzing of phase characteristics of temperature oscillations on the tubbing surface that is available for observing. To compute the phase characteristics, the digital lock-in correlation method is used. In the article an influence on the phase characteristics of heating frequency, heating time and noise is investigated. For mathematical processing of noisy data, the algorithm, based on using the reference temperature distribution on the tubbing surface covering the defect-free lining, is developed. This algorithm consists of the Kalman filter, the Rauch-Tung-Striebel smoothing procedure and the smoothing spline method with criterial choosing of the smoothing parameter. An efficiency of the proposed approach is illustrated by results of numerical experiments.