| This dissertation establishes a novel data-based fault detection approach, which effectively monitors process anomalies without explicit use of analytical model. The supervisory device is based on the detection of inconsistency among model sets for different process stages. This work bridges several gaps between the recent advancements in mathematical programming and the corresponding applications in process engineering. The strengths of this approach lay in the implementation and integration of three emerging strategies: an interior-point method (IPM) for efficient solution to large-scale linear programming (LP) problems; a homogeneous self-dual model that embeds a divergent infeasible problem in a convergent feasible problem; and a new warm-start strategy that exploits information in the previous solution for a sequence of slightly perturbed LPs.; The treatment of the LP is geared toward the latest efficient implementations. Practical applications confront three major challenges: handling large-scale and highly degenerate cases, detecting infeasibility, and employing warm-start. The traditional simplex method is replaced by IPM, avoiding intractable boundary complexity of large LPs; A homogeneous and self-dual algorithm is proposed, providing an affirmative certificate of infeasibility, a known initial feasible solution, and better numerical stability; An innovative warm-start strategy is developed based on optimal basis, substantially accelerating the solution of the next slightly disturbed LP. For perturbed LPs, a novel sensitivity study of optimal basis indicates that the optimal basis remains unchanged if perturbations stay in certain bounds for the next disturbed problem. This forms the foundation of the warm-start strategy: recovering an optimal basis from an IPM solution and starting new problem from the previous optimal basis.; Combining applications of path-following method, homogeneous self-dual model, basis identification, and warm-start, this dissertation presents applications for a continuous, multi-input multi-output, nonlinear model. The simulation experiments demonstrate that the approaches are efficient and practical. This work can be synthesized or extended to a wide range of on-line applications where efficiency is crucial, for example, model predictive control, on-line estimation, adaptive control, and real-time identification. |
