BURA Collection:
http://buratest.brunel.ac.uk/handle/2438/8629
2019-09-21T12:02:12ZHigh-order in time discontinuous Galerkin finite element methods for linear wave equations
http://buratest.brunel.ac.uk/handle/2438/15332
Title: High-order in time discontinuous Galerkin finite element methods for linear wave equations
Authors: Al-Shanfari, Fatima
Abstract: In this thesis we analyse the high-order in time discontinuous Galerkin nite element method (DGFEM) for second-order in time linear abstract wave equations. Our abstract approximation analysis is a generalisation of the approach introduced by Claes Johnson (in Comput. Methods Appl. Mech. Engrg., 107:117-129, 1993), writing the second order problem as a system of fi rst order problems. We consider abstract spatial (time independent) operators, highorder in time basis functions when discretising in time; we also prove approximation results in case of linear constraints, e.g. non-homogeneous boundary data. We take the two steps approximation approach i.e. using high-order in time DGFEM; the discretisation approach in time introduced by D Schötzau (PhD thesis, Swiss Federal institute of technology, Zürich, 1999) to fi rst obtain the semidiscrete scheme and then conformal spatial discretisation to obtain the fully-discrete formulation. We
have shown solvability, unconditional stability and conditional a priori error estimates within our abstract framework for the fully discretized problem. The skew-symmetric spatial forms arising in our abstract framework for the semi- and fully-discrete schemes do not full ll the underlying assumptions in D. Schötzau's work. But the semi-discrete and fully discrete forms satisfy an Inf-sup condition, essential for our proofs; in this sense our approach is also a generalisation of D. Schötzau's work. All estimates are given in a norm in space and time which is weaker than the Hilbert norm belonging to our abstract function spaces, a typical complication in evolution problems. To the best of the author's knowledge, with the approximation approach we used, these stability and a priori error estimates with their abstract structure have not been shown before for the abstract variational formulation used in this thesis. Finally we apply our abstract framework to the acoustic and an elasto-dynamic linear equations with non-homogeneous Dirichlet boundary data.
Description: This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London2017-01-01T00:00:00ZData analysis for improved risk assessment in underground pipelines
http://buratest.brunel.ac.uk/handle/2438/15166
Title: Data analysis for improved risk assessment in underground pipelines
Authors: Anes-Arteche, Francisco
Abstract: This thesis describes research relating to data analysis for improved risk assessment in buried pipelines. The kind of pipelines being considered includes onshore underground pipelines. External corrosion in buried pipelines is often complex to understand due to the diversity of factors affecting the corrosion process and in many cases, these pipelines operate in hostile environments. They may be less susceptible to failure and their failure may have different consequences in relation to aboveground pipelines. However, there is a limitation with respect what inspection techniques are efficient and therefore the assessment process is more difficult to be carried out. One of the major integrity risks to aging pipelines is the degradation and failure of the protective coating, leading to external corrosion. A commonly used approach for the assessment of external corrosion risk of buried pipelines is based on measurements from indirect inspections which are used to assess the likelihood of external corrosion. The underlying assumption is that indirect measurements can provide data to reliably identify corrosion defects on the pipeline, and prioritise defects according to their risk to pipeline integrity. One established method to determine the condition of the pipeline coating is to use an above-ground technique, such as DCVG, to locate the severity of the any coating defects, that may be present on a pipeline. Whilst the location aspect of this technique is very accurate and reliable, the severity may not correlate very well with the actual size of the coating defect when examined after excavation. Therefore, there is a need to refine the coating defect sizing model to provide a better indication of the severity of coating defects. However, there is little available research carried out to investigate this in a systematic manner. A further area of uncertainty relates to the correlation between the indirect inspection measurements, and the severity of the corrosion found following excavation. The development and refinement of regression models to address this link is required to ensure better corrosion predictions and improved inspection plans. The aim of the research described in this thesis is to analyse the external corrosion phenomenon in underground pipelines through the analysis of data from inspection reports and soil surveys. This aim has been achieved through specific studies at TWI, two of which are described in this thesis. The contribution to knowledge of the research included in this thesis is the improvement on the understanding of pipeline coating condition and external corrosion phenomenon in underground pipelines through the analysis of data from inspection reports and soil survey. Also, the identification of key factors affecting external corrosion along the probability distribution function, including factors that affect the initiation of corrosion and factors which have more importance in cases of severe corrosion. The novelty of the research herein presented relies in the application of quantile regression to pipeline data combined with soil properties which has never been applied before. The results improve the understanding of pipeline coating condition and external corrosion in underground pipelines. Also, it proposes suggestions for improving the interpretation of the NACE ECDA SP-0502 standard which may lead to significant savings in the pipeline industry.
Description: This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London2017-01-01T00:00:00ZBoundary-domain integral equation systems for the stokes system with variable viscosity and diffusion equation in inhomogeneous media
http://buratest.brunel.ac.uk/handle/2438/14521
Title: Boundary-domain integral equation systems for the stokes system with variable viscosity and diffusion equation in inhomogeneous media
Authors: Fresneda-Portillo, Carlos
Abstract: The importance of the Stokes system stems from the fact that the Stokes system is the stationary linearised form of the Navier Stokes system [Te01, Chapter1]. This linearisation is allowed when neglecting the inertial terms at a low Reinolds numbers Re << 1. The Stokes system essentially models the behaviour of a non - turbulent viscous fluid. The mixed interior boundary value problem related to the compressible Stokes system is reduced to two different BDIES which are equivalent to the original boundary value problem. These
boundary-domain integral equation systems (BDIES) can be expressed in terms of surface and volume parametrix-based potential type operators whose properties are also analysed in appropriate Sobolev spaces. The invertibility and Fredholm properties related to the matrix operators that de ne the BDIES are
also presented. Furthermore, we also consider the mixed compressible Stokes system with variable
viscosity in unbounded domains. An analysis of the similarities and differences with regards to the bounded domain case is presented. Furthermore, we outline the mapping properties of the surface and volume parametrix-based potentials in weighted Sobolev spaces. Equivalence and invertibility results still hold under certain decay conditions on the variable coeffi cient The last part of the thesis refers to the mixed boundary value problem for the stationary heat transfer partial di erential equation with variable coe cient. This BVP is reduced to a system of direct segregated parametrix-based Boundary-Domain Integral Equations (BDIEs). We use a parametrix different from the one employed by Chkadua, Mikhailov and Natroshvili in the paper [CMN09].
Mapping properties of the potential type integral operators appearing in these equations are presented in appropriate Sobolev spaces. We prove the equivalence between the original BVP and the corresponding BDIE system. The invertibility and Fredholm properties of the boundary-domain integral operators are also analysed in both bounded and unbounded domains.
Description: This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London2016-01-01T00:00:00ZDiscrete Weibull regression model for count data
http://buratest.brunel.ac.uk/handle/2438/14476
Title: Discrete Weibull regression model for count data
Authors: Kalktawi, Hadeel Saleh
Abstract: Data can be collected in the form of counts in many situations. In other words, the number of deaths from an accident, the number of days until a machine stops working or the number of annual visitors to a city may all be considered as interesting variables for study. This study is motivated by two facts; first, the vital role of the continuous Weibull distribution in survival analyses and failure time studies. Hence, the discrete Weibull (DW) is introduced analogously to the continuous Weibull distribution, (see, Nakagawa and Osaki (1975) and Kulasekera (1994)). Second, researchers usually focus on modeling count data, which take only non-negative integer values as a function of other variables. Therefore, the DW, introduced by Nakagawa and Osaki (1975), is considered to investigate the relationship between count data and a set of covariates. Particularly, this DW is generalised by allowing one of its parameters to be a function of covariates. Although the Poisson regression can be considered as the most common model for count data, it is constrained by its equi-dispersion (the assumption of equal mean and variance). Thus, the negative binomial (NB) regression has become the most widely used method for count data regression. However, even though the NB can be suitable for the over-dispersion cases, it cannot be considered as the best choice for modeling the under-dispersed data. Hence, it is required to have some models that deal with the problem of under-dispersion, such as the generalized Poisson regression model (Efron (1986) and Famoye (1993)) and COM-Poisson regression (Sellers and Shmueli (2010) and Sáez-Castillo and Conde-Sánchez (2013)). Generally, all of these models can be considered as modifications and developments of Poisson models. However, this thesis develops a model based on a simple distribution with no modification. Thus, if the data are not following the dispersion system of Poisson or NB, the true structure generating this data should be detected. Applying a model that has the ability to handle different dispersions would be of great interest. Thus, in this study, the DW regression model is introduced. Besides the exibility of the DW to model under- and over-dispersion, it is a good model for inhomogeneous and highly skewed data, such as those with excessive zero counts, which are more disperse than Poisson. Although these data can be fitted well using some developed models, namely, the zero-inated and hurdle models, the DW demonstrates a good fit and has less complexity than these modifed models. However, there could be some cases when a special model that separates the probability of zeros from that of the other positive counts must be applied. Then, to cope with the problem of too many observed zeros, two modifications of the DW regression are developed, namely, zero-inated discrete Weibull (ZIDW) and hurdle discrete Weibull (HDW) models. Furthermore, this thesis considers another type of data, where the response count variable is censored from the right, which is observed in many experiments. Applying the standard models for these types of data without considering the censoring may yield misleading results. Thus, the censored discrete Weibull (CDW) model is employed for this case. On the other hand, this thesis introduces the median discrete Weibull (MDW) regression model for investigating the effect of covariates on the count response through the median which are more appropriate for the skewed nature of count data. In other words, the likelihood of the DW model is re-parameterized to explain the effect of the predictors directly on the median. Thus, in comparison with the generalized linear models (GLMs), MDW and GLMs both investigate the relations to a set of covariates via certain location measurements; however, GLMs consider the means, which is not the best way to represent skewed data. These DW regression models are investigated through simulation studies to illustrate their performance. In addition, they are applied to some real data sets and compared with the related count models, mainly Poisson and NB models. Overall, the DW models provide a good fit to the count data as an alternative to the NB models in the over-dispersion case and are much better fitting than the Poisson models. Additionally, contrary to the NB model, the DW can be applied for the under-dispersion case.
Description: This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London2017-01-01T00:00:00Z