A new method based on the principles of self-organization is designed. For researcher, the method does not require to set up initial model of the spectrum. A criterion of correspondence between the experimental and model spectra is evaluation of empirical risk. Result of calculation is a set of optimal spectra models proposed to the researcher. Our tests for a number of experimental spectra showed a high efficiency of the method. The method is used for analysis of experimental Mössbauer spectra of Fe$_{10}$C austenite. As compared with already known expansions, we obtained a new accurate expansion of the measured spectrum into one singlet and two doublet lines. To interpret the results, we performed first-principle FLAPW calculations of electronic structure and hyperfine interactions in several ordered Fe$_{32}$C$_{2}$ structures, which model FeC$_{0.0625}$ austenite. There is a good agreement between the measured data and the theoretical calculations.