Reducing the uncertainty of ULS load estimates in offshore structural design


  • Joao Cruz Yavin Four Consultants
  • Mairead Atcheson Cruz Yavin Four Consultants
  • Michele Martini Yavin Four Consultants



Wave Energy Converter (WEC), concept design, load analysis, extreme load, Ultimate Limit State (ULS), uncertainty quantification, goodness-of-fit tests


The design process of any offshore structure, including Wave Energy Converters (WECs), aims to assess a series of critical conditions, often encapsulated in the concept of ‘limit states’, that define the ‘design boarders’ across which a structure is unlikely to respond satisfactorily, potentially leading to functional failure(s). The Load and Resistance Factor Design (LRFD) method aims to quantify such ‘design boarders’ with adequate safety margins on both the loading and the resistance sides of the design inequality. An inherent risk of such approach is that the definition of ‘adequate’ may be clouded by multiple sources of uncertainty, making it challenging to assess if a system is likely to be under- or over-designed from inception.

Although overall guidance for the design process of a WEC can be sought from related industries – see e.g. [1], and while noting that generic guidance for WEC design is available in e.g. [2], there is at present limited (practical) guidance on how to derive estimates of long-term return period loads. In recent work, comparative assessments of different load estimation methods have been made, illustrating the dependence of the outputs on the underlying method – see e.g. [3]. Additionally, and in connection with the assessment of extreme loads acting on WECs, the load post-processing methodology was identified in [4] as the major contributor to the uncertainty in Ultimate Limit State (ULS) load estimates.

This paper presents a novel post-processing methodology to assess the uncertainty when estimating ULS loads acting on an offshore structure. To assess which  statistical distributions are best suited to estimate long-term extreme loads, goodness-of-fit tests were performed using a series of input load time-series. The methodology was applied to evaluate the 50-year return load acting on the foundation of a generic Submerged Pressure Differential (SPD) WEC, based on the generic configuration originally defined in [5]. Results suggest that current conventional practices based on visual inspection(s) may lead to the selection of non-representative fitting functions which, in turn, likely lead to inaccurate extreme load estimations.

Ultimately, the methodology described in this paper aims to contribute to a probabilistic approach to the definition of suitable safety factors, which in turn is expected to reduce the uncertainty in key design metrics and the risk of either under- or over-design.

This study was conducted as part of the H2020 VALID and H2020 IMPACT projects.


[1] DNVGL-ST-0437. (2016). Loads and site conditions for wind turbines.

[2] IEC/TS 62600-2. (2019). Marine energy — Wave, tidal and other water current converters Part 2: Design requirements for marine energy systems.

[3] Michelen, C., Coe, R. Comparison of Methods for Estimating Short-Term Extreme Response of Wave Energy Converters, Sandia National Laboratories, SAND2015-6890C.

[4] Atcheson, M., Cruz, J., Martins, T., Johannesson, P., Svensson, T. (2019). Quantification of load uncertainties in the design process of a WEC, Proc. 13th European Wave and Tidal Energy Conference (EWTEC 2019), Naples, Italy.

[5] Babarit, A., Hals, J., Muliawan, M.J. et al. (2012). Numerical benchmarking study of a selection of wave energy converters. Renewable Energy 41, 44-63.



How to Cite

J. Cruz, M. . Atcheson Cruz, and M. . Martini, “Reducing the uncertainty of ULS load estimates in offshore structural design”, Proc. EWTEC, vol. 15, Sep. 2023.