## Computational Methods for Time-Variant Structural Reliability Analysis

### Christian Bucher

Vienna University of Technology, Vienna, Austria

The life-cycle oriented design of structures requires the consideration of time-dependent effects such as structural deterioration, maintenance and repair, or even substantial change of environmental conditions (traffic loads, storms, etc.). All these factors are essentially random and should be characterized in probabilistic terms. Consequently, the safety and reliability of a structure can be assessed suitably only in terms of a time-dependent probabilistic analysis. Since typically the failure probabilities of well-designed structures are very small (as compared to unity), special care must be taken choose computational methods suitable for the computations (or better, estimation) of such small probabilities.

The paper will provide an overview of both well-established methods as well as more recent developments of procedures to provide structural reliability estimates. They will be discussed from the viewpoint of suitability for time-dependent problems (such as e.g. those due to material degradation) and from the perspective of life-cycle oriented structural optimization (such as e.g. minimization of total life-time cost).

As always, Monte-Carlo based strategies are most promising in terms of general applicability. In particular, there are virtually no restrictions concerning the treatment of nonlinear effects and arbitrarily time-varying influences. Unfortunately, the computational effort may be prohibitively large. Advanced Monte-Carlo methods can frequently reduce the effort required, however, due to the additional knowledge required about the problem, the estimates may become more unstable. Alternative methods based on deterministic computations (such as the First Order Reliability Method) rely on certain regularity conditions (e.g. differentiability) of the limit state function, which cannot be guaranteed in many practical cases. Finally, there are methods based on representing the structural behavior in terms of surrogate models (e.g. response surfaces or lower-order models) which shift the problem from the evaluation of the structural reliability to the problem of finding suitable simple approximation models for the structural responses. Obviously, the gain in computational efficiency is closely related to the loss in accuracy.

Several simple application examples will demonstrate how the individual methods can be rated with respect to the categories outlined above.