Online Monitoring of Thermoacoustic Eigenmodes in Annular Combustion Systems Based on a State Space Model

2016 ◽  
Author(s):  
Driek Rouwenhorst ◽  
Jakob Hermann ◽  
Wolfgang Polifke
Keyword(s):  
State Space ◽  
Online Monitoring ◽  
Stability Margin ◽  
Surrogate Data ◽  
Modal Identification ◽  
Mode Shapes ◽  
Space Representation ◽  
Azimuthal Mode ◽  
Noise Characteristics ◽  
Combustion Systems

Thermoacoustic instabilities have the potential to restrict the operability window of annular combustion systems, primarily as a result of azimuthal modes. Azimuthal acoustic modes are composed of counter-rotating wave pairs, which form traveling modes, standing modes, or combinations thereof. In this work, a monitoring strategy is proposed for annular combustors that accounts for azimuthal mode shapes. Output-only modal identification has been adapted to retrieve azimuthal eigenmodes from surrogate data, resembling acoustic measurements on an industrial gas turbine. Online monitoring of decay rate estimates can serve as a thermoacoustic stability margin, while the recovered mode shapes contain information that can be useful for control strategies. A low-order thermoacoustic model is described, requiring multiple sensors around the circumference of the combustor annulus to assess the dynamics. This model leads to a second order state space representation with stochastic forcing, which is used as the model structure for the identification process. Four different identification approaches are evaluated under different assumptions, concerning noise characteristics and preprocessing of the signals. Additionally, recursive algorithms for online parameter identification are tested.

Online Monitoring of Thermoacoustic Eigenmodes in Annular Combustion Systems Based on a State-Space Model

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
D. Rouwenhorst ◽  
J. Hermann ◽  
W. Polifke
Keyword(s):  
State Space ◽  
Online Monitoring ◽  
Stability Margin ◽  
Surrogate Data ◽  
Modal Identification ◽  
Mode Shapes ◽  
Space Representation ◽  
Azimuthal Mode ◽  
Noise Characteristics ◽  
Combustion Systems

Thermoacoustic instabilities have the potential to restrict the operability window of annular combustion systems, primarily as a result of azimuthal modes. Azimuthal acoustic modes are composed of counter-rotating wave pairs, which form traveling modes, standing modes, or combinations thereof. In this work, a monitoring strategy is proposed for annular combustors, which accounts for azimuthal mode shapes. Output-only modal identification has been adapted to retrieve azimuthal eigenmodes from surrogate data, resembling acoustic measurements on an industrial gas turbine. Online monitoring of decay rate estimates can serve as a thermoacoustic stability margin, while the recovered mode shapes contain information that can be useful for control strategies. A low-order thermoacoustic model is described, requiring multiple sensors around the circumference of the combustor annulus to assess the dynamics. This model leads to a second-order state-space representation with stochastic forcing, which is used as the model structure for the identification process. Four different identification approaches are evaluated under different assumptions, concerning noise characteristics and preprocessing of the signals. Additionally, recursive algorithms for online parameter identification are tested.

Thermoacoustic Modeling and Control of Multi Burner Combustion Systems

2003 ◽  
Author(s):  
Bruno Schuermans ◽  
Valter Bellucci ◽  
Christian Oliver Paschereit
Keyword(s):  
State Space ◽  
Time Domain ◽  
Dynamic Models ◽  
Hybrid Approach ◽  
Combustion Process ◽  
Analytical Techniques ◽  
Space Representation ◽  
Element Analysis ◽  
Modal Expansion ◽  
Combustion Systems

Thermoacoustic interactions in industrial combustion systems are difficult to model because they involve complex interactions between several physical mechanisms. In order to obtain dynamic models of such systems, a hybrid approach is used: numerical, experimental and analytical techniques are combined to describe the system. The system is modeled as a modular network, where the input–output relation of the modules can be based on analytic models, experimental data or numerical analysis. The modules are represented as state-space realizations. A modal expansion technique is used to obtain a state-space representation of the acoustic propagation through complex 3-dimensional geometries. The modal expansion can be based on an analytic model (for relatively simple volumes), or on a finite element analysis (for geometries of any complexity). Modules that are very complex, such as the acoustic behavior of the combustion process itself, are modeled using a combined experimental and analytic approach. The method is not restricted to symmetries of any kind: configurations with geometrically or operationally different burners are simulated. The state-space network approach allows for time domain simulations, including non-linearities. An active controller has been synthesized for an (hypothetical) annular multi burner combustion system. The controller uses spatial filtering to decompose the acoustic field to its individual modes. The modes are then controlled using an H∞ control algorithm. Time domain simulations of this control system demonstrate the effectiveness of this method, even in the presence of non-linear saturation and parametric errors.

H2 Optimization of Damped-Vibration Absorbers for Suppressing Vibrations in Beams With Constrained Minimization

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Murat Tursun ◽  
Eşref Eşkinat
Keyword(s):  
State Space ◽  
The State ◽  
Mode Shapes ◽  
Space Representation ◽  
Vibration Absorbers ◽  
State Space Representation ◽  
Lagrange’S Equation ◽  
System Output ◽  
External Forces ◽  
Mass Spring

Vibration absorbers are efficient and robust tools for reducing vibration and noise. Researchers use various alternative approaches and validate their methods with examples consisting of mass-spring-damper systems. Focusing on the minimization of the vibration amplitudes via passive absorber approach, a new and efficient method for calculating the optimum parameters of N absorbers attached to a uniform beam with M mode shapes (where N and M are any positive integers) has been developed. First, for the most general case, dissipation due to damping, kinetic, and potential energy and the effects of external forces are analyzed. The Lagrange's equation is used to provide the state space representation of the system. State space representation of a system with N absorbers and M mode shapes is composed. On the basis of the state space representation and the Lyapunov function, the H2 norm of the transfer function of the system is utilized in the newly developed optimization package. The system output is minimized by the optimization algorithm and displayed with a comparison between cases without an absorber and with randomly selected absorber parameters. As a conclusion, with the help of this method for calculation of optimal absorber parameters, one can easily design a mechanical system according to design criteria.

Design Methodology for Microelectromechanical Systems. Case Study: Torsional Scanner Mirror

2006 ◽  
Vol 129 (10) ◽  
pp. 1023-1030 ◽  
Author(s):  
Faik Can Meral ◽  
Ipek Basdogan
Keyword(s):  
State Space ◽  
Microelectromechanical Systems ◽  
Transfer Functions ◽  
State Space Model ◽  
The State ◽  
Mode Shapes ◽  
Design Parameters ◽  
Space Representation ◽  
Disturbance Analysis ◽  
Disturbance Torque

Future optical microsystems, such as microelectromechanical system (MEMS) scanners and micromirrors, will extend the resolution and sensitivity offered by their predecessors. These systems face the challenge of achieving nanometer precision subjected to various disturbances. Predicting the performance of such systems early in the design process can significantly impact the design cost and also improve the quality of the design. Our approach aims to predict the performance of such systems under various disturbance sources and develop a generalized design approach for MEMS structures. In this study, we used ANSYS for modeling and dynamic analysis of a torsional MEMS scanner mirror. ANSYS modal analysis results, which are eigenvalues (natural frequencies) and eigenvectors (mode shapes), are used to obtain the state-space representation of the mirror. The state-space model of the scanner mirror was reduced using various reduction techniques to eliminate the states that are insignificant for the transfer functions of interest. The results of these techniques were compared to obtain the best approach to obtain a lower order model that still contains all the relevant dynamics of the original model. After the model size is reduced significantly, a disturbance analysis is performed using Lyapunov approach to obtain root-mean-square values of the mirror rotation angle under the effect of a disturbance torque. The magnitude levels of the disturbance torque are obtained using an experimental procedure. The disturbance analysis framework is combined with the sensitivity analysis to determine the critical design parameters for optimizing the system performance.

scholarly journals Nonlinear analysis of magnetospheric data Part I. Geometric characteristics of the AE index time series and comparison with nonlinear surrogate data

1999 ◽  
Vol 6 (1) ◽  
pp. 51-65 ◽  
Author(s):  
G. P. Pavlos ◽  
M. A. Athanasiu ◽  
D. Kugiumtzis ◽  
N. Hatzigeorgiu ◽  
A. G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
State Space ◽  
Null Hypothesis ◽  
Surrogate Data ◽  
Statistical Testing ◽  
Geometrical Parameters ◽  
Geometric Characteristics ◽  
Geometrical Characteristics ◽  
Ae Index ◽  
Index Time Series

Abstract. A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper) and dynamical characteristics (Part II, which is the work a separate paper), and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index) signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.

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