Model-based solution techniques for the source localization problem in distributed parameter systems

Graduation date: 1999In this thesis, three model-based methods are presented for finding the location of a\ud point source with possibly time-varying strength for a class of distributed parameter systems.\ud The first method involves off-line numerical computation of the time-response data\ud at the sensor(s) from all possible source locations and functions of source strength, and\ud comparison of these data with actual measurements. The second method involves approximation\ud of the infinite-dimensional distributed parameter system by a finite-dimensional\ud lumped parameter system: the partial differential and/or integral equations describing\ud the distributed parameter system are replaced by a set of ordinary differential equations,\ud which are obtained through finite difference or finite element methods. The resulting\ud model is used to construct an auto-regressive (AR) filter that takes the sensor data as inputs\ud and produces a scalar output whose value determines the source location. The third\ud method involves off -line steady-state solution of an adjoint problem based on the dual\ud system model. The solutions are used to construct localization functions whose contours,\ud corresponding to a set of sensor data, provide an estimate of the source location. For each\ud method, the sensor data evaluation algorithm is presented, and analysis is given of appropriate\ud sensor placement and the minimal required number of sensors. The robustness\ud of each method to sensor noise and modeling inaccuracies is studied, and techniques to\ud improve robustness are discussed. These techniques include strategic sensor placement to\ud reduce sensitivity to noise and modeling inaccuracies, and prioritization of sensor data in\ud the data evaluation algorithms. In all three methods, a minimal amount of on-line computation is required. The methods are applied to the two-dimensional heat conduction problem with Robin's boundary conditions, and their performances are tested via computer simulations. The thesis concludes with a discussion of the relative strengths and shortcomings of each method and suggestions for future research