State Estimation Techniques in Nonlinear Distributed Parameter Systems

In order to characterize physical systems for the purpose of design and control, physical insight (in the form of mathematical models) and direct observations are usually combined within a state estimation framework. By making the best use of the available information, state estimation techniques allow to improve the quality of the knowledge of the state variables. There is a considerable number of methods for nonlinear lumped-parameter models available in the literature, but there has been little focus on distributed-parameter systems. In this work, we propose a systematic extension of existing techniques to such models and we investigate a new hybrid technique. Among existing techniques, our focus is on particle filtering (PF) and moving horizon estimation (MHE) due to their particular and complementary set of characteristics: MHE is robust and naturally handles constraints and parameter estimation, but can be too expensive for large systems, and current implementations require the distributions to be Gaussian; PF is faster and no assumptions are required about the shape of the distributions, but its robustness is not always sufficient and it does not address constraints or estimation of parameters within its framework. Full discretisation of the set of PDEs describing the system is employed. The viability of the extension is demonstrated through a flow assurance case study involving estimation of temperature and pressure profiles in deepwater subsea pipelines. Given the complementary characteristics of MHE and PF, in the sense that the weak points of one technique are the strong points of the other, we have recently developed a hybrid estimator whose goal is to provide a balanced compromise between the pure methods: robust, fast and capable of addressing parameter estimation, constraints and non Gaussian statistics. This estimator and its application to distributed parameter systems are presented. The excellent performance and versatility of the proposed approach is shown using the aforementioned flow assurance case study.