Novel Data-Centric Methods for Inference and Prediction of Large-Scale Complex Systems

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Modern jet engines are the most expensive components on an aircraft and are engineered to be extremely reliable at great cost (up to $25 million per engine). Yet they can still experience unexpected catastrophic failure, resulting in tragedy and loss of life. In order to monitor engine health and performance, each engine is equipped with about 100 sensors that measure a variety of performance parameters, from the pressure and temperature of the engine gas path to vibration of the rotating components. Stall and Surge are dynamic instabilities in which the engine compressor adds energy to small oscillations in the system, increasing their amplitude, potentially causing damage to engine components. In order to prevent damage, compressor instability must be controlled, which requires state estimators (filters), for example, to estimate the mass flow rate from the pressure measurement. The goals of the proposed research are to develop novel mathematical and statistical methods that exploit new sensing capabilities on engines for (i) determining instability limits; (ii) developing advanced reduced-order filters based on nonlinear models with uncertainties; and (iii) developing new anomaly-detection schemes and quickest-change detection algorithms.******Theme 1 of the proposal focuses on the dynamics and control of compressor instabilities based on a full partial differential equation (PDE) model with uncertainty. A number of obstacles must be resolved to advance filtering of nonlinear PDE models. A key issue is computational complexity, which requires model-order reduction techniques to enable efficient processing and data assimilation. The filtering strategy proposed here will lead to better feedback control of compressor instabilities, thus preventing damage to engine components and lengthening their life-span.******Theme 2, the proposed quickest-change detection, will be a vital procedure for engine performance monitoring. Engine data are obtained sequentially: as long as the engine is categorized as being in a ``normal state," its operation continues unabated. However, once a change in state has occurred, that change must be detected as soon as possible, while minimizing false detections. The statistical methods proposed, which involve optimizing the tradeoff between a measure of detection delay and a measure of the frequency of false alarms, will yield new means for understanding the behavior of large-scale complex systems at a higher level of sophistication.******The proposed data-centric methods will also open new research perspectives and domains that rely heavily on measurements for system monitoring and control. Finally, the broad educational impacts of this proposal include cross-disciplinary training of graduate students in a variety of mathematical, statistical and computational techniques and in some of the most complex technologies built, and international collaboration.