A deformation model of flexible, high area-to-mass ratio debris under perturbations and validation method

A new type of space debris was recently discovered by Schildknecht in near -geosynchronous orbit (GEO). These objects were later identified as exhibiting properties associated with High Area-to-Mass ratio (HAMR) objects. According to their brightness magnitudes (light curve), high rotation rates and composition properties (albedo, amount of specular and diffuse reflection, colour, etc), it is thought that these objects are multilayer insulation (MLI). Observations have shown that this debris type is very sensitive to environmental disturbances, particularly solar radiation pressure, due to the fact that their shapes are easily deformed leading to changes in the Area-to-Mass ratio (AMR) over time. This thesis proposes a simple effective flexible model of the thin, deformable membrane with two different methods. Firstly, this debris is modelled with Finite Element Analysis (FEA) by using Bernoulli-Euler theory called “Bernoulli model”. The Bernoulli model is constructed with beam elements consisting 2 nodes and each node has six degrees of freedom (DoF). The mass of membrane is distributed in beam elements. Secondly, the debris based on multibody dynamics theory call “Multibody model” is modelled as a series of lump masses, connected through flexible joints, representing the flexibility of the membrane itself. The mass of the membrane, albeit low, is taken into account with lump masses in the joints. The dynamic equations for the masses, including the constraints defined by the connecting rigid rod, are derived using fundamental Newtonian mechanics. The physical properties of both flexible models required by the models (membrane density, reflectivity, composition, etc.), are assumed to be those of multilayer insulation. Both flexible membrane models are then propagated together with classical orbital and attitude equations of motion near GEO region to predict the orbital evolution under the perturbations of solar radiation pressure, Earth’s gravity field, luni-solar gravitational fields and self-shadowing effect. These results are then compared to two rigid body models (cannonball and flat rigid plate). In this investigation, when comparing with a rigid model, the evolutions of orbital elements of the flexible models indicate the difference of inclination and secular eccentricity evolutions, rapid irregular attitude motion and unstable cross-section area due to a deformation over time. Then, the Monte Carlo simulations by varying initial attitude dynamics and deformed angle are investigated and compared with rigid models over 100 days. As the results of the simulations, the different initial conditions provide unique orbital motions, which is significantly different in term of orbital motions of both rigid models. Furthermore, this thesis presents a methodology to determine the material dynamic properties of thin membranes and validates the deformation of the multibody model with real MLI materials. Experiments are performed in a high vacuum chamber (10-4 mbar) replicating space environment. A thin membrane is hinged at one end but free at the other. The free motion experiment, the first experiment, is a free vibration test to determine the damping coefficient and natural frequency of the thin membrane. In this test, the membrane is allowed to fall freely in the chamber with the motion tracked and captured through high velocity video frames. A Kalman filter technique is implemented in the tracking algorithm to reduce noise and increase the tracking accuracy of the oscillating motion. The forced motion experiment, the last test, is performed to determine the deformation characteristics of the object. A high power spotlight (500-2000W) is used to illuminate the MLI and the displacements are measured by means of a high resolution laser sensor. Finite Element Analysis (FEA) and multibody dynamics of the experimental setups are used for the validation of the flexible model by comparing with the experimental results of displacements and natural frequencies.

Quantification of air quality in space and time and its effects on health

The long-term adverse effects on health associated with air pollution exposure can be estimated using either cohort or spatio-temporal ecological designs. In a cohort study, the health status of a cohort of people are assessed periodically over a number of years, and then related to estimated ambient pollution concentrations in the cities in which they live. However, such cohort studies are expensive and time consuming to implement, due to the long-term follow up required for the cohort. Therefore, spatio-temporal ecological studies are also being used to estimate the long-term health effects of air pollution as they are easy to implement due to the routine availability of the required data. Spatio-temporal ecological studies estimate the health impact of air pollution by utilising geographical and temporal contrasts in air pollution and disease risk across $n$ contiguous small-areas, such as census tracts or electoral wards, for multiple time periods. The disease data are counts of the numbers of disease cases occurring in each areal unit and time period, and thus Poisson log-linear models are typically used for the analysis. The linear predictor includes pollutant concentrations and known confounders such as socio-economic deprivation. However, as the disease data typically contain residual spatial or spatio-temporal autocorrelation after the covariate effects have been accounted for, these known covariates are augmented by a set of random effects. One key problem in these studies is estimating spatially representative pollution concentrations in each areal which are typically estimated by applying Kriging to data from a sparse monitoring network, or by computing averages over modelled concentrations (grid level) from an atmospheric dispersion model. The aim of this thesis is to investigate the health effects of long-term exposure to Nitrogen Dioxide (NO2) and Particular matter (PM10) in mainland Scotland, UK. In order to have an initial impression about the air pollution health effects in mainland Scotland, chapter 3 presents a standard epidemiological study using a benchmark method. The remaining main chapters (4, 5, 6) cover the main methodological focus in this thesis which has been threefold: (i) how to better estimate pollution by developing a multivariate spatio-temporal fusion model that relates monitored and modelled pollution data over space, time and pollutant; (ii) how to simultaneously estimate the joint effects of multiple pollutants; and (iii) how to allow for the uncertainty in the estimated pollution concentrations when estimating their health effects. Specifically, chapters 4 and 5 are developed to achieve (i), while chapter 6 focuses on (ii) and (iii). In chapter 4, I propose an integrated model for estimating the long-term health effects of NO2, that fuses modelled and measured pollution data to provide improved predictions of areal level pollution concentrations and hence health effects. The air pollution fusion model proposed is a Bayesian space-time linear regression model for relating the measured concentrations to the modelled concentrations for a single pollutant, whilst allowing for additional covariate information such as site type (e.g. roadside, rural, etc) and temperature. However, it is known that some pollutants might be correlated because they may be generated by common processes or be driven by similar factors such as meteorology. The correlation between pollutants can help to predict one pollutant by borrowing strength from the others. Therefore, in chapter 5, I propose a multi-pollutant model which is a multivariate spatio-temporal fusion model that extends the single pollutant model in chapter 4, which relates monitored and modelled pollution data over space, time and pollutant to predict pollution across mainland Scotland. Considering that we are exposed to multiple pollutants simultaneously because the air we breathe contains a complex mixture of particle and gas phase pollutants, the health effects of exposure to multiple pollutants have been investigated in chapter 6. Therefore, this is a natural extension to the single pollutant health effects in chapter 4. Given NO2 and PM10 are highly correlated (multicollinearity issue) in my data, I first propose a temporally-varying linear model to regress one pollutant (e.g. NO2) against another (e.g. PM10) and then use the residuals in the disease model as well as PM10, thus investigating the health effects of exposure to both pollutants simultaneously. Another issue considered in chapter 6 is to allow for the uncertainty in the estimated pollution concentrations when estimating their health effects. There are in total four approaches being developed to adjust the exposure uncertainty. Finally, chapter 7 summarises the work contained within this thesis and discusses the implications for future research.