Estimation of Time-dependent Reliability of Suspension Bridge Cables

The reliability of the main cable of a suspension bridge is crucial to the reliability of the entire bridge. Throughout the life of a suspension bridge, its main cables are subject to corrosion due to various factors, and the deterioration of strength is a slowly evolving and dynamic process. The goal of this research is to find the pattern of how the strength of steel wires inside a suspension bridge cable changes with time. Two methodologies are proposed based on the analysis of five data sets which were collected by testing pristine wires, artificially corroded wires, and wires taken from three suspension bridges: Severn Bridge, Forth Road Bridge and Williamsburg Bridge. The first methodology is to model wire strength as a random process in space whose marginal probability distribution and power spectral density evolve with time. Both the marginal distribution and the power spectral density are parameterized with time-dependent parameters. This enables the use of Monte Carlo methods to estimate the failure probability of wires at any given time. An often encountered problem -- the incompatibility between the non-Gaussian marginal probability distribution and prescribed power spectral density -- which arises when simulating non-Gaussian random processes using translational field theory, is also studied. It is shown by copula theory that the selected marginal distribution imposes restrictions on the selection of power spectral density function. The second methodology is to model the deterioration rate of wire strength as a stochastic process in time, under Ito's stochastic calculus framework. The deterioration rate process is identified as a mean-reversion stochastic process taking non-negative values. It is proposed that the actual deterioration of wire strength depends on the deterioration rate, and may also depend on the state of the wire strength itself. The probability distribution of wire strength at any given time can be obtained by integrating the deterioration rate process. The model parameters are calibrated from the available data sets by matching moments or minimizing differences between probability distributions.