Algorithms for UAS insertion in civil air space

One of the most interesting challenge of the next years will be the Air Space Systems automation. This process will involve different aspects as the Air Traffic Management, the Aircrafts and Airport Operations and the Guidance and Navigation Systems. The use of UAS (Uninhabited Aerial System) for civil mission will be one of the most important steps in this automation process. In civil air space, Air Traffic Controllers (ATC) manage the air traffic ensuring that a minimum separation between the controlled aircrafts is always provided. For this purpose ATCs use several operative avoidance techniques like holding patterns or rerouting. The use of UAS in these context will require the definition of strategies for a common management of piloted and piloted air traffic that allow the UAS to self separate. As a first employment in civil air space we consider a UAS surveillance mission that consists in departing from a ground base, taking pictures over a set of mission targets and coming back to the same ground base. During all mission a set of piloted aircrafts fly in the same airspace and thus the UAS has to self separate using the ATC avoidance as anticipated. We consider two objective, the first consists in the minimization of the air traffic impact over the mission, the second consists in the minimization of the impact of the mission over the air traffic. A particular version of the well known Travelling Salesman Problem (TSP) called Time-Dependant-TSP has been studied to deal with traffic problems in big urban areas. Its basic idea consists in a cost of the route between two clients depending on the period of the day in which it is crossed. Our thesis supports that such idea can be applied to the air traffic too using a convenient time horizon compatible with aircrafts operations. The cost of a UAS sub-route will depend on the air traffic that it will meet starting such route in a specific moment and consequently on the avoidance maneuver that it will use to avoid that conflict. The conflict avoidance is a topic that has been hardly developed in past years using different approaches. In this thesis we purpose a new approach based on the use of ATC operative techniques that makes it possible both to model the UAS problem using a TDTSP framework both to use an Air Traffic Management perspective. Starting from this kind of mission, the problem of the UAS insertion in civil air space is formalized as the UAS Routing Problem (URP). For this reason we introduce a new structure called Conflict Graph that makes it possible to model the avoidance maneuvers and to define the arc cost function of the departing time. Two Integer Linear Programming formulations of the problem are proposed. The first is based on a TDTSP formulation that, unfortunately, is weaker then the TSP formulation. Thus a new formulation based on a TSP variation that uses specific penalty to model the holdings is proposed. Different algorithms are presented: exact algorithms, simple heuristics used as Upper Bounds on the number of time steps used, and metaheuristic algorithms as Genetic Algorithm and Simulated Annealing. Finally an air traffic scenario has been simulated using real air traffic data in order to test our algorithms. Graphic Tools have been used to represent the Milano Linate air space and its air traffic during different days. Such data have been provided by ENAV S.p.A (Italian Agency for Air Navigation Services).

Plasticity in body and peripersonal space representations

A successful interaction with objects in the environment requires integrating information concerning object-location with the shape, dimension and position of body parts in space. The former information is coded in a multisensory representation of the space around the body, i.e. peripersonal space (PPS), whereas the latter is enabled by an online, constantly updated, action-orientated multisensory representation of the body (BR) that is critical for action. One of the critical features of these representations is that both PPS and BR are not fixed, but they dynamically change depending on different types of experience. In a series of experiment, I studied plastic properties of PPS and BR in humans. I have developed a series of methods to measure the boundaries of PPS representation (Chapter 4), to study its neural correlates (Chapter 3) and to assess BRs. These tasks have been used to study changes in PPS and BR following tool-use (Chapter 5), multisensory stimulation (Chapter 6), amputation and prosthesis implantation (Chapter 7) or social interaction (Chapter 8). I found that changes in the function (tool-use) and the structure (amputation and prosthesis implantation) of the physical body elongate or shrink both PPS and BR. Social context and social interaction also shape PPS representation. Such high degree of plasticity suggests that our sense of body in space is not given at once, but it is constantly constructed and adapted through experience.

Bayesian space-time data fusion for real-time forecasting and map uncertainty

Environmental computer models are deterministic models devoted to predict several environmental phenomena such as air pollution or meteorological events. Numerical model output is given in terms of averages over grid cells, usually at high spatial and temporal resolution. However, these outputs are often biased with unknown calibration and not equipped with any information about the associated uncertainty. Conversely, data collected at monitoring stations is more accurate since they essentially provide the true levels. Due the leading role played by numerical models, it now important to compare model output with observations. Statistical methods developed to combine numerical model output and station data are usually referred to as data fusion. In this work, we first combine ozone monitoring data with ozone predictions from the Eta-CMAQ air quality model in order to forecast real-time current 8-hour average ozone level defined as the average of the previous four hours, current hour, and predictions for the next three hours. We propose a Bayesian downscaler model based on first differences with a flexible coefficient structure and an efficient computational strategy to fit model parameters. Model validation for the eastern United States shows consequential improvement of our fully inferential approach compared with the current real-time forecasting system. Furthermore, we consider the introduction of temperature data from a weather forecast model into the downscaler, showing improved real-time ozone predictions. Finally, we introduce a hierarchical model to obtain spatially varying uncertainty associated with numerical model output. We show how we can learn about such uncertainty through suitable stochastic data fusion modeling using some external validation data. We illustrate our Bayesian model by providing the uncertainty map associated with a temperature output over the northeastern United States.

Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

Constraints on neutrino mass fraction using Redshift Space Distortions

Redshift Space Distortions (RSD) are an apparent anisotropy in the distribution of galaxies due to their peculiar motion. These features are imprinted in the correlation function of galaxies, which describes how these structures distribute around each other. RSD can be represented by a distortions parameter $\beta$, which is strictly related to the growth of cosmic structures. For this reason, measurements of RSD can be exploited to give constraints on the cosmological parameters, such us for example the neutrino mass. Neutrinos are neutral subatomic particles that come with three flavours, the electron, the muon and the tau neutrino. Their mass differences can be measured in the oscillation experiments. Information on the absolute scale of neutrino mass can come from cosmology, since neutrinos leave a characteristic imprint on the large scale structure of the universe. The aim of this thesis is to provide constraints on the accuracy with which neutrino mass can be estimated when expoiting measurements of RSD. In particular we want to describe how the error on the neutrino mass estimate depends on three fundamental parameters of a galaxy redshift survey: the density of the catalogue, the bias of the sample considered and the volume observed. In doing this we make use of the BASICC Simulation from which we extract a series of dark matter halo catalogues, characterized by different value of bias, density and volume. This mock data are analysed via a Markov Chain Monte Carlo procedure, in order to estimate the neutrino mass fraction, using the software package CosmoMC, which has been conveniently modified. In this way we are able to extract a fitting formula describing our measurements, which can be used to forecast the precision reachable in future surveys like Euclid, using this kind of observations.