Design optimization is crucial as offshore structures are exposed to deeper and harsher marine conditions. The structure behaviour is dependent on several joint environmental parameters (wind, wave, currents, etc.). Environmental contours are useful representations to provide multivariate design conditions. However, these contours may lead to different design points depending on the method used to compute them, and thus may be misleading to structural engineer.

In this work, we propose to use a response meta-model for the inter-comparison of some state-of-the-art methods available for modelling multivariate extremes, in order to provide a straightforward methodology, focusing on the derivation of three-dimensional contours. The considered case study focuses on the tension in a mooring line of a semi-submersible platform. In a first step, the key met-ocean parameters and the associated load model of the tension in the mooring line are set-up. Several multivariate extreme analysis methods are then applied to derive the environmental contours. These methods are chosen in order to cover all the possible dependence cases, from extremal dependence to extremal independence. Conditional Extreme and several extreme value dependence function models are investigated. The physical-space Huseby contouring method is used to derive environmental surface. A comparison with the extreme load extrapolated from the meta-model is provided to assess the performance of each method.