Helen K. Qammar

Adaptive estimation and synchronization of chaotic systems

Abstract In this Letter the recently introduced method to synchronize deterministic chaotic systems is generalized by means of concepts in adaptive control.

Stall Precursor Identification in High-Speed Compressor Stages Using Chaotic Time Series Analysis Methods

This paper presents a new technique for precursor identification in high-speed compressors. The technique is a pseudo-correlation integral method referred to as the correlation method. To provide a basis for comparison, the traveling wave energy technique, which has been used extensively to study prestall data, is also briefly presented and applied. The correlation method has a potential advantage over the traveling wave energy method because it uses a single sensor for detection. It also requires no predisposition about the expected behavior of the data to detect changes in the behavior of the compressor. Both methods are used in this study to identify stall precursive events in the pressure fluctuations measured from circumferential pressure transducers located at the front face of the compressor rig. The correlation method successfully identified stall formation or changes in the compressor dynamics from data captured from four different configurations of a NASA Lewis single-stage high-speed compressor while it was transitioned from stable operation into stall. This paper includes an exposition on the use of nonlinear methods to identify stall precursors, a description of the methodologies used for the study, information on the NASA high-speed compressor rig and experimental data acquisition, and results from the four compressor configurations. The experimental results indicate that the correlation method provides ample warning of the onset of rotating stall at high speed, in some tests on the order of 2000 rotor revolutions. Complementary features of the correlation method and the traveling wave energy method are discussed, and suggestions for future developments are made.

Investigation of Pre-stall Mode and Pip Inception in High-Speed Compressors Through the Use of Correlation Integral

Five high-speed compressor configurations are used to identify pre-stall pressure signal activity under clean and distorted inlet conditions, and under steady injection and controlled injection conditions. Through the use of a nonlinear statistic called correlation integral, variations in the compressor dynamics are identified from the pre-stall pressure activity far before variations (modal or pip) are observed visually in the wall static pressure measurements. The correlation integral not only discerns changing dynamics of these compressors prior to stall, but is now used to measure the strength of the tip flow field for these five high-speed compressors. Results show that correlation integral value changes dramatically when the stall inception is modal; and it changes less severely when the stall inception is through pip disturbances. This algorithm can therefore distinguish from the pre-stall pressure traces when a machine is more likely to stall due to pips versus modes. When used in this manner, the correlation integral thus provides a measure of tip flow strength. The algorithm requires no predisposition about the expected behavior of the data in order to detect changing dynamics in the compressor; thus, no pre-filtering is necessary. However, by band-pass filtering the data, one can monitor changing dynamics in the tip flow field for various frequency regimes. An outcome of this is to associate changes in correlation integral value directly with frequency specific events occurring in the compressor, i.e., blade length scale events versus long length scale acoustic events. The correlation integral provides a potential advantage over linear spectral techniques The correlation integral provides a potential advantage over linear spectral techniques because a single sensor is used for detection and analysis of the instabilities.

SYSTEM IDENTIFICATION AND MODEL-BASED CONTROL OF A CHAOTIC SYSTEM

In this paper the control of a hyper2chaotic system is considered to show the role of system identification techniques in developing a model for effective control of highly complex systems. An indirect adaptive control scheme is considered and it is shown that simple prediction models which cannot possibly represent the dynamics of the chaotic system lead to stable control. Furthermore, it is shown that higher dimensional prediction models which more closely represent the chaotic process dynamics lead to controlled systems with sparse and disjoint basins of attraction for the desired steady state solution. The use of highly nonlinear models also results in a complex pattern of convergence to the desired state.

Dynamical complexity arising in the adaptive control of a chaotic system

Abstract In this Letter unique properties of an indirect adaptive controller designed to drive a chaotic logistic system to a steady state are presented and compared to published results.

INDIRECT ADAPTIVE CONTROL OF A CHAOTIC SYSTEM

Abstract The adaptive control of a simple chaotic system to a steady reference is investigated. An indirect adaptive control scheme with least-mean-squares (LMS) parameter estimation yields a fractal basin boundary between stable and unstable control. This boundary appears self-similar, indicative of a fractal structure, and has a fractal dimension of 2.61. Adaptive control using a least-squares (LS) estimator appears globally stable with the rate of adaptation a complex function of the distance from the desired set point. The effect of control parameters, noise and a step-change perturbation of the system are also reported.

PRACTICAL CONSIDERATIONS ON THE CALCULATION OF THE UNCERTAINTY EXPONENT AND THE FRACTAL DIMENSION OF BASIN BOUNDARIES

The calculation of the uncertainty exponent as defined in Grebogi et al. [1983] is examined in detail, and it is modified to provide a more robust estimate of the fractal dimension of basin boundaries. Practical considerations of using the uncertainty exponent method are provided.

Stall Precursor Identification in High Speed Compressor Stages Using Chaotic Time Series Analysis Methods

This paper presents a new technique for precursor identification in high speed compressors. The technique is a pseudo-correlation integral method referred to as the correlation method. To provide a basis for comparison, the traveling wave energy technique, which has been used extensively to study pre-stall data, is also briefly presented and applied. The correlation method has a potential advantage over the traveling wave energy method because it uses a single sensor for detection. It also requires no predisposition about the expected behavior of the data to detect “changes” in the behavior of the compressor. Both methods are used in this study to identify stall procursive events in the pressure fluctuations measured from circumferential pressure transducers located at the front face of the compressor rig. The correlation method successfully identified stall formation or changes in the compressor dynamics from data captured from four different configurations of a NASA Lewis single stage high speed compressor while it was transitioned from stable operation into stall. This paper includes an exposition on the use of nonlinear methods to identify stall precursors, a description of the methodologies used for the study, information on the NASA high speed compressor rig and experimental data acquisition, and results from the four compressor configurations. The experimental results indicate that the correlation method provides ample warning of the onset of rotating stall at high speed, in some tests on the order of 2000 rotor revolutions. Complementary features of the correlation method and the traveling wave energy method are discussed, and suggestions for future developments are made.Copyright

Manifolds and control of chaotic systems

Abstract Because of the erratic oscillations in chaotic systems, it is often desirable to control them to a steady state. When a controller is added it creates a new dynamical system whose properties are influenced by the underlying chaotic system. Increasing the amount of control has a dramatic effect on the manifolds and the basin for the desired stable steady state. Therefore, it is important to understand the effect of the unique properties of chaotic systems when developing new controller designs to yield optimum performance.

Investigation of Pre-Stall Mode and Pip Inception in High Speed Compressors Through the Use of Correlation Integral

Five high speed compressor configurations are used to identify pre-stall pressure signal activity under clean and distorted inlet conditions, and under steady injection and controlled injection conditions. Through the use of a nonlinear statistic called correlation integral, variations in the compressor dynamics are identified from the pre-stall pressure activity far before variations (modal or pip) are observed visually in the wall static pressure measurements. The correlation integral not only discerns changing dynamics of these compressors prior to stall, but is now used to measure the strength of the tip flow field for these five high speed compressors. Results show that correlation integral value changes dramatically when the stall inception is modal; and it changes less severely when the stall inception is through pip disturbances. This algorithm can therefore distinguish from the pre-stall pressure traces when a machine is more likely to stall due to pips versus modes. When used in this manner, the correlation integral thus provides a measure of tip flow strength. The algorithm requires no predisposition about the expected behavior of the data in order to detect changing dynamics in the compressor, thus no pre-filtering is necessary. However, by band-pass filtering the data, one can monitor changing dynamics in the tip flow field for various frequency regimes. An outcome of this is to associate changes in correlation integral value directly to frequency specific events occurring in the compressor, i.e. blade length scale events versus long length scale acoustic events. The correlation integral provides a potential advantage over linear spectral techniques because a single sensor is used for detection and analysis of the instabilities.Copyright