State Estimation for diffusion systems using a Karhunen-Loeve-Galerkin Reduced-Order Model

摘要: This thesis focuses on generating a continuous estimate of state using small number sensors for process modeled by the diffusion partial differential equation(PDE). In biological systems oxygen in tissue is well described equation, also known biologists as Fick’s first law. Mass transport many other materials are PDE such CO2, cell signaling factors, glucose and biomolecules. Estimating more formidable than that system ordinary equations (ODEs). While variables ODE finite number, distributed spatial domain infinite number. Reduction to which tractable estimation will be accomplished through use Karhunen-Loeve-Galerkin method model order reduction. The reduction broken into two steps, (i) determine an appropriate set basis functions (ii) project onto candidate functions. Karhunen-Loeve expansion used decompose observations principle modes composing dynamics. may obtained numerical simulation or physical experiments encompass all dynamics reduced-order expected reproduce. then projected linear Galerkin method, giving ODEs describe from procedure with Kalman filter state. Performance estimator investigated several experiments. Fidelity different numbers compared against solution considered true problem. efficiency empirical analytical examined. reducedii noiseless noisy system. Effects sensor placement quantity evaluated. A test platform was developed study track simple non-biological allows dye gelatin monitored camera. An concentration throughout entire volume point sensors, i.e. pixels selected evaluated actual captured provide means empirically diffusion-reaction associated estimators.