Studies in non-Gaussian analysis

This thesis presents general methods in non-Gaussian analysis in infinite dimensional spaces. As main applications we study Poisson and compound Poisson spaces. Given a probability measure μ on a co-nuclear space, we develop an abstract theory based on the generalized Appell systems which are bi-orthogonal. We study its properties as well as the generated Gelfand triples. As an example we consider the important case of Poisson measures. The product and Wick calculus are developed on this context. We provide formulas for the change of the generalized Appell system under a transformation of the measure. The L² structure for the Poisson measure, compound Poisson and Gamma measures are elaborated. We exhibit the chaos decomposition using the Fock isomorphism. We obtain the representation of the creation, annihilation operators. We construct two types of differential geometry on the configuration space over a differentiable manifold. These two geometries are related through the Dirichlet forms for Poisson measures as well as for its perturbations. Finally, we construct the internal geometry on the compound configurations space. In particular, the intrinsic gradient, the divergence and the Laplace-Beltrami operator. As a result, we may define the Dirichlet forms which are associated to a diffusion process. Consequently, we obtain the representation of the Lie algebra of vector fields with compact support. All these results extends directly for the marked Poisson spaces.

Low cost non-intrusive home energy monitoring

This thesis presents a low cost non-intrusive home energy monitor built on top of Non-Intrusive Load Monitoring (NILM) concepts and techniques. NILM solutions are already considered low cost alternatives to the big majority of existing commercial energy monitors but the goal here is to make its cost even lower by using a mini netbook as a whole in one solution. The mini netbook is installed in the homes main circuit breaker and computes power consumption by reading current and voltage from the built-in sound card. At the same time, feedback to the users is provided using the 11’’ LCD screen as well as other built-in I/O modules. Our meter is also capable of detecting changes in power and tries to find out which appliance lead to that change and it is being used as part of an eco-feedback platform that was build to study the long terms of energy eco-feedback in individuals. In this thesis the steps that were taken to come up with such a system are presented, from the basics of AC power measurements to the implementation of an event detector and classifier that was used to disaggregate the power load. In the last chapter results from some validation tests that have been performed are presented in order to validate the experiment. It is believed that such a system will not only be important as an energy monitor, but also as an open system than can be easily changed to accommodate and test new or existing nonintrusive load monitoring techniques.