Bayesian approach applied for thermoacoustic inverse problem

The paper presents a solution for the thermoacoustic inverse problem using the Bayesian approach. Using some probabilistic information about the disturbance of data, the method takes into account the uncertainty of measurements in parameter identification. All variables, both measurements and estimated parameters are treated as random variables. The solution of this task is an expected value of the numerically generated Markov chain from appropriate probability distribution. In this work, the thermoacoustic inverse problem in which the heat release rate was identified on the basis of information obtained from the pressure measurements on the walls of the combustion chamber. The problem discussed has been formulated and the method used for its solution has been presented. Apart from the Bayesian approach, the Marcov chain Monte Carlo algorithm (used for obtaining the Markov chain in a numerical way) is also presented. To verify this methodology, two numerical examples formulated as the thermoacoustic inverse problem are solved and obtained results are presented.