Copula-based models in railroad maintenance and safety analysis

Date
2018
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University of Delaware
Abstract
The American railroad industry has been a primary stakeholder in the economic development of the nation for close to two centuries. The railroads account for over two-fifths of freight revenue ton-miles and transports about a third of all national exports. To ensure good operable conditions of rail infrastructure particularly the track, the railroads have spent more than 40\% of their revenue on capital expenditure and maintenance since industry deregulation. Due to budgetary and high logistical constraints, there has been a gradual shift to predictive maintenance strategies with railroads planning track geometry maintenance activities in advance. To employ such strategies, there is the need to know beforehand the effectiveness of maintenance activities which can be evaluated by the amount of improvement or recovery in track geometry condition. ☐ Well executed maintenance invariably improves operational efficiency and safety which are primary objectives of the railroads. The huge investment in maintenance led to all-time lows in train derailment rate, accident rate, and collision rate recorded in recent years. Despite their relatively low frequency, derailments remain a major concern for the railroads due to their high consequences which include loss of life and property, disruption of services, injury, and destruction to the natural environment. It is therefore important to carefully examine train derailment severity in order to minimize these ramifications. ☐ In many railroad applications of data analysis; non-normality of data occurs in several forms. For example, exploratory data analysis of both derailment data and track geometry data showed that the marginal and joint distributions of the variables were not normal. Conventional correlation analysis is generally not suitable for analyzing the dependencies between variables with non-normality, tail dependence, asymmetric dependence, skewness and other nonlinearities. Furthermore, conventional correlation analysis also fails to consider the underlying dependence between multiple response variables which may be skewed or discrete in nature. This dissertation focuses on the formulation of copula-based methodologies to analyze railroad maintenance and safety applications considering the underlying dependence between the variables of interest. Copulas allow for the separate modeling of arbitrary marginal distributions and the dependence structure. Copulas are suitable for modeling various forms of dependence and can be employed in the generation of large volumes of data. ☐ Three railroad engineering case studies are undertaken in this dissertation. In the first case study, a bivariate copula-based approach is developed to evaluate the tamping recovery of track geometry parameters such as surface, alignment, cross level, gage, and warp considering the underlying dependence between the variables of interest. In the second case study, a mixed copula-based regression model is developed which simultaneously models the monetary damage and number of derailed cars conditional on a set of covariates that might affect both derailment severity outcomes. Marginal generalized linear regression models are combined with a bivariate copula which characterizes the dependence between the two responses. In the third and final case study, vine copula models, a cascade of bivariate copulas as building blocks, are used to model high-dimensional dependencies within the derailment severity data. ☐ Results from this dissertation provide greater insight and comprehension of the train derailment severity and track geometry recovery phenomena considering various forms of dependence between the variables of interest. These results will aid decision making which would help reduce the consequences of train derailments as well as improve track maintenance strategies.
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