Identification of thermoacoustic dynamics that exhibit limit cycle behavior is needed to gain a better intuitive feel of the system, to design complex control strategies, and to validate modeling efforts. Limit cycle oscillations arise in thermoacoustic systems due to the coupling between a nonlinear heat release process and the acoustic dynamics of the combustor. This response arises in lean premixed gaseous power generating turbines and is a concern due to the detrimental effect of the pressure oscillations on the structural integrity of the combustor. Due to the volatile environment intrinsic in the combustor, multiple sensing apparatuses are not available. Therefore, in the current study, an identification approach is assessed considering only a single output from the thermoacoustic system. As a means to further investigate the thermoacoustic limit cycle behavior, a scaled version of the industry-based turbine was constructed. By anchoring a flame halfway from end-to-end of a closed-open tube, a similar nonlinear response is achieved. A harmonic balance technique that linearly incorporates the nonlinearity is developed which uses frequency entrainment to offer sufficient information for the identification. Its validity is assessed on a model, which is based on known dynamics of the thermoacoustic system. The structure of the identification algorithm is based on a two-mode acoustic model with both dynamics and nonlinearity in the feedback loop. The limitations of using only a two-mode identification structure for a system with more than two modes is discussed as well as future efforts that may alleviate this problem. / Master of Science