Time-Dependent Reliability Calculations Approximated by a Lower and Upper Bound Method to Determine Time-To-Failure Curve for Optimization of Interventions

Abstract

The optimization of the timing of repair interventions on civil engineering structures is ideally based on the minimization of the total life-cycle cost. An important part of the total life-cycle cost is the expected failure cost, which can be calculated based on the lifetime function describing the probability density of the time-to-failure. However, for deteriorating structures, the determination of the lifetime function is not straightforward as it requires solving a time-dependent reliability problem. This can be computationally expensive for more complex structures and hence a challenge for the optimization algorithm that is searching for the optimal maintenance strategy. To overcome this problem, the probability of failure for time-dependent reliability problems can be approximated by time-independent lower and upper bounds that are much easier to quantify. In this work, it is investigated whether the proposed maintenance strategy changes significantly if the bounds are used instead of the more exact and numerically more expensive solution. The results show that the lower bound approach is generally a better option than the upper bound approach to achieve a close-to-optimal solution.