Estimation of Dynamical Thermoacoustic Modes Using an Output Only Observer Kalman Filter-Based Identification Algorithm

Abstract

Thermoacoustic instabilities have plagued the operation of gas turbine engines for years and significant research is being conducted in detecting and understanding them. In this paper, an output only identification technique is employed for a noise induced dynamical system representing combustion instability behaviour. This approach is called the Output only Observer Kalman filter identification (O3KID) and its first step solves for least squares from a set of algebraic equations constructed from just the measured output. The least squares solution gives the Markov parameters (impulse response) and the output residuals. The subsequent step takes the Markov parameters or the residuals to solve for the system matrices using any deterministic sub-space identification method. In using this direct non-iterative two-step algorithm, it is possible to estimate the eigenmodes and damping coefficients from output measured data. To validate the algorithm, a system of independent harmonic oscillators, excited by random noise is used to generate surrogate data representing pressure oscillations in a combustor prior to an instability. The error in estimating the eigen frequencies and damping are <1%. This fast direct approach could be used to provide an early warning indicator in industrial gas turbines by tracking the rate of damping of dominant eigenmodes. Additionally, saving the state space parameters periodically can serve as a data-lean option to track changes of the dynamics and across a gas turbine fleet.