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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.

In this mixed-methods study we identify situations that impact students' decisions to withdraw from a course and examine their affective reasoning and attitudes toward course withdrawal. Exploring students' decision-making processes through the lens of self-authorship, we show that students frequently seek information from people with whom they have a personal rather than academic relationship, make decisions with little awareness of academic consequences, and often experience a feeling of dissonance when withdrawing from courses, even describing themselves as “quitters.” Our results lead to recommendations that can assist academic advisors in developing meaningful interventions that advance students' decision-making abilities and intellectual development.

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 because a single sensor is used for detection and analysis of the instabilities.

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.

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.

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.