Global wave load combinations by cross-spectral methods

E. Alfred Mohammed*, H. S. Chan, S. E. Hirdaris

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

18 Citations (Scopus)


This paper presents a cross spectral stochastic analysis methodology for the determination of the combination of global wave-induced dynamic loads by taking into account uncertainties associated with the wave heading, the joint probabilities of the wave environment and the correlations between different global wave-induced dynamic loads. The methodology considers the use of bivariate probability density functions (the cross-spectral probabilistic approach) or the co-variances of two random variables with their associated derivatives (the cross-spectral Hamilton's method) and assumes only rigid body hydrodynamic actions under steady forward speed conditions. The design extreme values of principal global wave-induced load components and their combinations for a container ship progressing in irregular seaways are predicted using these two cross-spectral methods together with the short-term and long-term statistical formulations. It is shown that in general terms both cross-spectral analysis methods can be employed to assess the effects of loads in ship design and reliability analysis. However, the cross-spectral Hamilton's method predicts slightly higher load combinations than the cross-spectral probabilistic approach.

Original languageEnglish
Pages (from-to)131-151
Number of pages21
JournalMarine Structures
Issue number1
Publication statusPublished - 1 Dec 2012
MoE publication typeA1 Journal article-refereed


  • Cross-spectral analysis
  • Global wave-induced loads
  • Loads combination


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