Session: 05-01 Advanced Controls for Propulsion Systems

Paper Number: 80650

80650 - Estimation of Dynamical Thermoacoustic Modes Using an Output Only Observer Kalman Filter-Based Identification (O3KID) Algorithm 

Thermoacoustic instabilities have plagued the operation of gas turbine engines for years [DR1] 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. Combustor data is often times modulated by background noise, whose characteristics are not well defined apriori. Especially in an output only identification approach, the characteristics of the pure system dynamics and background stochastic noise are not independent.  In order to simplify our problem and identify both deterministic and stochastic components, a two-step identification using state space modelling is implemented. The data is transformed to accommodate an observer, which predicts the current state of a system from its previous states. The observer takes the form of a Kalman filter and in solving for the Kalman filter gain would solve the original problem yielding all the system matrices of the state space model. 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 this paper, classical methods such as the Eigenvalue Realization Algorithm (ERA) using the Markov parameters and Deterministic Intersection (DI) using the output residuals are employed to solve for the system matrices. 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. [DR2] [DR3]  The O3KID algorithm could identify the eigenmodes with exactly the degrees of freedom required to define it i.e., a system with three harmonic oscillators could be defined with a 6-order model, which implies 6 coefficients. The error in estimating the eigen frequencies and damping are <1%. On top, the stochastic background and the dynamics of the system could be independently identified. 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.

 

 

Presenting Author: nikhil balasubramanian IfTA GmbH

Presenting Author Biography: Nikhil is a doctorate student working at IfTA GmbH and Technical university of Munich. He is a Marie Curie fellow pursuing his PhD as part of the ITN Polka.

Authors:

nikhil balasubramanian IfTA GmbH
Driek Rouwenhorst IfTA GmbH
Jakob Hermann IfTA GmbH