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Data assimilation using sequential Monte Carlo methods in hydrological applications
Get PDFHydrologic Data Assimilation concerns the application of state estimation methods to hydrologic models. The hydrologic models used in this dissertation correspond to a lumped conceptual model (rainfall-runoff model) and a distributed physically-based model (land surface-atmosphere transfer scheme). Hydrologic systems are highly nonlinear with complex dynamics. Therefore, nonlinear/non-Gaussian estimation techniques should be used in the inference of the states and/or parameters of the hydrologic models. In this sense, sequential Monte Carlo methods (a.k.a. particle filters) have captured the interest of the scientific community and nowadays are widely utilized in complex state estimation problems. This dissertation introduces two data assimilation methods which are based on Kalman and particle filtering theory: the ensemble Gaussian particle filter and the standard particle filter with parameter resampling. The first hydrologic variable to be assimilated is the discharge of water at the outlet of the Zwalm catchment which is located in East-Flanders. The second variable of interest is the volumetric soil moisture content in the study area located in the Grand Duchy of Luxembourg. These variables are assimilated separately in experiments with different setups and different study areas. Overall, the results indicate an improvement in the estimation of the model output flows when the proposed methods are applied to specific hydrologic data assimilation problems
Fractional order models of the human respiratory system
Get PDFThe fractional calculus is a generalization of classical integer-order integration and derivation to fractional (non-integer) order operators. Fractional order (FO) models are those models which contain such fractional order operators. A common representation of these models is in frequency domain, due to its simplicity. The dynamical systems whose model can be approximated in a natural way using FO terms, exhibit specific features, such as viscoelasticity, diffusion and a fractal structure; hence the respiratory system is an ideal application for FO models.
Although viscoelastic and diffusive properties were intensively investigated in the respiratory system, the fractal structure was ignored. Probably one of the reasons is that the respiratory system does not pose a perfect symmetry, hence failing to satisfy one of the conditions for being a typical fractal structure. In the 70s, the respiratory impedance determined by the ratio of air-pressure and air-flow, has been introduced in a model structure containing a FO term. It has also been shown that the fractional order models outperform integer-order models on input impedance measurements. However, there was a lack of underpinning theory to clarify the appearance of the fractional order in the FO model structure.
The thesis describes a physiologically consistent approach to reach twofold objectives:
1. to provide a physiologically-based mathematical explanation for the necessity of fractional order models for the input impedance, and
2. to determine the capability of the best fractional order model to classify between healthy and pathological cases.
Rather than dealing with a specific case study, the modelling approach presents a general method which can be used not only in the respiratory system application, but also in other similar systems (e.g. leaves, circulatory system, liver, intestines). Furthermore, we consider also the case when symmetry is not present (e.g. deformations in the thorax - kyphoscoliose) as well as various pathologies. We provide a proof-of-concept for the appearance of the FO model from the intrinsic structure of the respiratory tree. Several clinical studies are then conducted to validate the sensitivity and specificity of the FO model in healthy groups and in various pathological groups
The knee joint motion in a force and position controlled knee rig : modeling, implementation and validation
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A Gentle Introduction to Model Based Predictive Control. Proceedings of the International Workshop on Constrained Control Systems, Univ. Federal de Santa Catarina, Brazil, 1998, pp.16.
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