@phdthesis{Neureither2019, author = {Neureither, Lara}, title = {Irreversible multi-scale diffusions: time scales and model reduction}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-50467}, school = {BTU Cottbus - Senftenberg}, year = {2019}, abstract = {In this work, we consider non-reversible multi-scale stochastic processes, described by stochastic differential equations, for which we review theory on the convergence behaviour to equilibrium and mean first exit times. Relations between these time scales for non-reversible processes are established, and, by resorting to a control theoretic formulation of the large deviations action functional, even the consideration of hypo-elliptic processes is permitted. The convergence behaviour of the processes is studied in a lot of detail, in particular with respect to initial conditions and temperature. Moreover, the behaviour of the conditional and marginal distributions during the relaxation phase is monitored and discussed as we encounter unexpected behaviour. In the end, this results in the proposal of a data-based partitioning into slow and fast degrees of freedom. In addition, recently proposed techniques promising accelerated convergence to equilibrium are examined and a connection to appropriate model reduction approaches is made. For specific examples this leads to either an interesting alternative formulation of the acceleration procedure or structural insight into the acceleration mechanism. For the model order reduction technique of effective dynamics, which uses conditional expectations, error bounds for non-reversible slow-fast stochastic processes are obtained. A comparison with the reduction method of averaging is undertaken, which, for non-reversible processes, possibly yields different reduced equations. For Ornstein-Uhlenbeck processes sufficient conditions are derived for the two methods (effective dynamics and averaging) to agree in the infinite time scale separation regime. Additionally, we provide oblique projections which allow for the sampling of conditional distributions of non-reversible Ornstein-Uhlenbeck processes.}, subject = {Model reduction; Non-reversible diffusions; Relative entropy; Convergence to steady state; Conditional expectation; Modellreduktion; Nicht-reversible Diffusionen; Relative Entropie; Konvergenz gegen den Gleichgewichtszustand; Bedingte Erwartung; Ordnungsreduktion; Molekulardynamik; Diffusionsprozess; Bedingter Erwartungswert}, language = {en} } @phdthesis{Osagie2023, author = {Osagie, Christian}, title = {Reliability assessment of onshore pipelines based on Bayesian inference}, doi = {10.26127/BTUOpen-6733}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-67338}, school = {BTU Cottbus - Senftenberg}, year = {2023}, abstract = {Reliability assessment of pipeline failure factors has become a major concern for industrial firms involved in the transmission of oil and gas, where the requirement to limit these failure factors and their consequences, such as maintenance costs, is particularly significant. Pipelines were constructed throughout time to include safety precautions in order to offer a theoretical minimal failure rate for the pipeline's whole life. This strategy also includes the management of various failure causes as well as routine-based maintenance to assure the dependability of pipelines during their service life. However, the requirement to reduce the impact of these failure factors on pipelines has bolstered the use of reliability evaluation of failure factors on petroleum pipelines. The purpose of this study is to evaluate the reliability of oil pipelines in Nigeria, with emphasis on proposing operational and technical changes to enhance their resilience against unexpected failures. The thesis uses the regular Poisson, empirical, and compound Poisson processes to describe the number of common failure causes owing to corrosion, third-party damage, mechanically induced failure, operational mistakes, and natural hazards in repairable systems. The statistical analysis results serve as the foundation for time to failure modeling of petroleum pipelines utilizing Bayesian inference of the three-parameter Exponentiated Weibull distribution. The thesis also includes reliability probabilistic methods for assessing the influence of uncertainties in pipelines by comparing the First order reliability method (FORM) with the Second order reliability method (SORM) with demonstration on five distinct petroleum pipelines. The probability of failure and the reliability index for the five pipelines were calculated, along with the target reliability. Additionally, the influence of specific pipeline design parameters on the probability of failure was analyzed through sensitivity analysis. This analysis helps identify which design factors have the most significant impact on the likelihood of pipeline failure, allowing for more informed decisions in pipeline design and maintenance practices. By understanding these influences, it is possible to enhance the overall reliability and safety of the pipeline infrastructure. The framework developed in this thesis can be applied to enhance the performance of existing pipelines and serve as a good foundation for the design and implementation of new pipelines and similar infrastructures.}, subject = {Uncertainty; Wahrscheinlichkeit; Oil and gas pipelines; Failures; Analysis; Probability; {\"O}l- und Gaspipelines; Ausf{\"a}lle; Analyse; Unsicherheit; Pipeline; Bayes-Verfahren; Zuverl{\"a}ssigkeit}, language = {en} }