Time-variant reliability-oriented structural optimization and a renewal model for life-cycle costing

Objective functions for discounted cost optimization based on a continuous renewal model for a series of cases are presented. They include failures and subsequent renewals by crossings of loading processes or random disturbances out of safe states of structural components, failures due to aging, non-constant benefit and damage functions, finite renewal times, repeated reconstructions at renewals and inspection and repair. A method for reliability-oriented time-variant structural optimization of separable (independent) series systems using first order reliability methods in standard space is developed generalizing theories proposed earlier for component problems and time-invariant series system problems in a special one-level approach. Certain improvements by taking account of dependencies among failure modes are also given. Numerical Laplace transforms are proposed for the treatment of aging components. A newly developed gradient-based algorithm solves the optimization problem. Some algorithmic details are discussed. The approach is demonstrated at two examples.