Location
M3 3103
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Dongchang Li | Applied Mathematics, University of À¶Ý®ÊÓƵ
Title
Quickest Change Detection in Nonlinear Hidden Markov Models Using a Generalized CUSUM Procedure
Abstract
Fault diagnosis in modern aircraft engines is crucial for monitoring due to the rising need for high performance and safety. Early detection of system changes within a controllable range can prevent significant breakdowns. It's essential to track jet engine states and detect real-time dynamic mode shifts. This thesis explores change detection theories and procedures to handle dynamic instabilities in jet engines. We use the Moore-Greitzer equation to model flow and pressure changes in axial-flow compressors, specifically focusing on a reduced planar system. The research addresses QCD problems in nonlinear hidden Markov models, using pressure rise coefficients as observational data. The standard QCD scheme doesn't apply, so we employ the generalized CUSUM procedure, where post-change distribution depends on an unknown change point, despite its non-recursive nature. We adopt standard filtering theory to approximate log-likelihood ratios with particle methods. To manage computational costs, we adjust the CUSUM-like procedure with an assumption of immediate change to enable recursion. This research focuses on how changes in the system excite shifts from a steady state to a new equilibrium or periodic oscillations. We assess the performance of generalized CUSUMs with particle filters through random simulations in surge modes of the Moore–Greitzer model with external forcing. Observations reveal similarities and differences between generalized CUSUMs and a special CUSUM that assumes immediate change, influenced by phase errors and the relationship of the steady state to the limit cycle. Signal noise mitigates phase effects of the limit cycle.
This research addresses change detection in the Moore-Greitzer PDE model, where disturbances in axial flow at the compressor inlet are combined with a modified ODE system. We simulate the PDE system by obtaining time series from a finite-dimensional Moore-Greitzer system using the Fourier spectral method. Employing proper orthogonal decomposition (POD), we reduce model dimensions while maintaining fidelity with fewer basis functions. The reduced model is validated by reconstructing the PDE system with $N$ POD modes capturing about 95% energy of the full model in $L^2$ inner product and $H^1$ Sobolev spaces. We examine generalized CUSUM statistics to detect dynamics change, using POD bases and particle filters, with simulations showing the effectiveness of CUSUM statistics using {\em in situ} and {\em a priori} POD modes. Validated reduced models implement the generalized CUSUM for stall detection in stochastic systems, showing the generalized CUSUM statistics are more effective and robust than recursive CUSUM-like procedures.