*Proceedings of the*

The 33rd European Safety and Reliability Conference (ESREL 2023)

3 – 8 September 2023, Southampton, UK

# Environmental Contours and Time Dependence

### Department of Mathematics, University of Oslo, Norway.

#### ABSTRACT

Environmental contours are widely used as a basis for e.g., ship design. Such contours are typically used in early design when the strength and failure properties of the object under consideration are not known. An environmental contour describes the tail properties of some relevant environmental variables, and is used as input to the design process. A methodology for constructing environmental contours based on the Rosenblatt transformation has beed used extensively. More recently alternative approach where environmental contours are constructed using Monte Carlo simulation have been developed. Typically, the strength of a structural design is chosen so that the expected return period of a failure event exceeds the desired lifetime of the structure. If time dependence in the environmental variables is neglected, the expected return period is simply the inverse of the failure probability. In a more realistic model, however, such dependence should be included. In this paper we describe a method for constructing an environmental contour where time dependence is taken into account. The method is illustrated with a simple numerical example.

*Keywords: *Structural reliability, Environmental contour, Structural design, Failure probability, Markov models, Autoregressive models.