Modeling and testing of temporal and non-linear dependence in a multivariate process system

This thesis presents the modeling and testing of temporal and spatial non-linear dependence among the process components in a process system. Due to interconnectivity among process units, the variables are highly correlated and dynamic. Accident models should capture these complex and dynamic behaviours of the components to predict accidents early. Fault tree, Dynamic fault tree, Bayesian network, Dynamic Bayesian network and Copula-based Bayesian network models have been selected to model these characteristics of the variables and develop the early prediction of accidents. At first, temporal dependency has been modeled and experimentally validated. The performances of dependence models are illustrated for accident analysis using Fault tree, Dynamic fault tree and Bayesian network models. Process datasets from a lab-scale pilot plant introducing faults into the system have been used for this purpose. The analysis shows that the inherent properties to capture different spatial (indirect dependencies) and temporal dependencies among process variables make the Bayesian network superior to Dynamic fault tree and the traditional fault tree models. Secondly, non-linear spatial dependence (modeled as covariate direct dependence) along with temporal dependence have been modeled to investigate accidents. A copula-based Bayesian network and traditional Bayesian network have been used to model direct dependence and the performances of the models are validated experimentally. A pilot plant has been used to perform experiments and collect process data sets. The results illustrate that, the copula function can capture the non-linear dependence among process variables. The integration of the copula function and Bayesian network can predict accident probability more efficiently than the traditional Bayesian network. The successful validation of the accident models confirms the evolving nature of the models capturing spatial and temporal dependence to address operational safety challenges in the process industries

Doctor of Philosophy

dissertationWater resources are limited and disproportionately distributed in time and place. Moreover, complex interactions among different components of the water system, changes in population and urbanization growth rates, and climate change have increased the uncertainty influencing water resource planning. The ultimate question arising for water managers considering the complexity of water systems is how to determine if management strategies are effective and improve the performance of a water system. Generally, decision-makers assess the system’s condition based on a univariate measure of reliability or vulnerability. However, these measures do not deliver sufficient information, and present a limited view about the system’s performance. There is a known need to study water resources in an integrated fashion to effectively manage for the present and the future. In this dissertation, a new comprehensive integrated modeling and performance assessment framework is offered. First, a new approach is designed to assess vulnerability of a water system based on important factors including exposure, sensitivity, severity, potential severity, social vulnerability, and adaptive capacity. Then, instead of an individual metric, the joint probability distribution of reliability and vulnerability based on copula function is developed to estimate a new index, the Water System Performance Index (WSPI), to evaluate the reliability and vulnerability of a water system simultaneously. To test the effectiveness of the framework and demonstrate the advances of the new performance index, a practical application is conducted for the Salt Lake City Department of Public Utilities (SLCDPU) water system. For this purpose, an integrated water resource management (IWRM) model is developed using system dynamics approach for the case study. Management alternatives are incorporated into the model using a decision support tool designed for use by water managers and stakeholders. Results of the study show an inconsistency in the degree of vulnerability between traditionally used and the new vulnerability assessment approaches. The use of the integrated model and new vulnerability approach is also shown to provide more informative guidance for decision makers evaluating alternative management strategies during failure events. Furthermore, results illustrate the effectiveness of the WSPI to identify critical conditions when there is a need for a combined measure of performance. In terms of water management decision making, the final results of this dissertation indicate centralized water storage solutions improve water system performance better than rainwater harvesting for the Salt Lake City case study

Tensor approximation of generalized correlated diffusions and applications

This thesis documents my research activity conducted in the past three years at the Department of Statistical Science at the University College London. My investigation is focused on functional-analytic methods applied to the characterization of generalized correlated Markov processes. The main objective of the research is to formalize the properties of such a class of stochastic processes when approximated in a tensor space. This lead to the development of a new interpretation of the correlation among processes that is exploited for the analysis of copula functions and their statistical properties

Dynamic multivariate loss and risk assessment of process facilities

Dynamic risk assessments (DRA) are the next generation of risk estimation approaches that help to enable safer operations of complex process systems in changing environments. By incorporating new evidences from systems in the risk assessment process, the DRA techniques ensure estimation of current risk. This thesis investigates the existing knowledge and technological challenges associated with dynamic risk assessment and proposes new methods to improve effective implementation of DRA techniques. Risk is defined as the combination of three attributes: what can go wrong, how bad could it be, and how often might it happen. This research evaluates the limitations of the methodologies that have been developed to answer the latter two questions. Loss functions are used in this work to estimate and model operational loss in process facilities. The application of loss functions provides the following advantages: (i) the stochastic nature of losses is taken into account; and (ii) the estimation of the operational loss in process facilities due to the deviation of key process characteristics (KPC) is conducted. Models to estimate reputational loss and significant elements of business interruption loss, which are usually ignored in the literature, are also provided. This research also presents a methodology to develop multivariate loss functions to measure the operational loss of multivariate process systems. For this purpose, copula functions are used to link the univariate loss functions and develop the multivariate loss functions. Copula functions are also used to address the existing challenge of loss aggregation for multiple-loss scenarios. Regarding the dynamic estimation of the probability of abnormal events, the Bayesian Network (BN) has usually been used in the literature. However, integrated safety analysis of hazardous process facilities calls for an understanding of both stochastic and topological dependencies, going beyond traditional BN analysis to study cause-effect relationships among major risk factors. This work presents a novel model based on the Copula Bayesian Network (CBN) for multivariate safety analysis of process systems, which addresses the main shortcomings of traditional BNs. The proposed CBN model offers great flexibility in probabilistic analysis of individual risk factors while considering their uncertainty and complex stochastic dependence. The research outcomes provide advanced methods for critical operations, such as the offshore operations in harsh environments, to be used in continuous improvement of processes and real-time risk estimation. Application of the proposed dynamic risk assessment framework, along with a proper safety culture, enhances the day-to-day risk-informed decision making process by constantly monitoring, evaluating and improving the process safety performance