Practical guidelines for multivariate analysis and design in coastal and off-shore engineering

• Practical guidelines to carry out a sensible multivariate analysis are outlined.
• A statistically consistent definition of multivariate return periods is presented.
• Strategies for coastal and off-shore structural multivariate design are shown.
• Critical multivariate design values of wave height and storm duration are calculated.
• Procedures for data randomization and random scenarios generation are introduced.

A frequent statistical problem in many coastal and off-shore engineering situations is to estimate the probability of structural failure expressed in terms of Return Period and Design Quantile. Usually, only the univariate approach is carried out to quantify the risk of failure. However, coastal and off-shore structures typically fail because of the occurrence of a critical combination of all the variables at play in a single sea storm: thus, it may be important to consider the joint occurrence of dangerous conditions. The present manuscript provides practical guidelines in order to carry out a sensible multivariate analysis of the available data, including a randomization procedure to cope with repeated observations. In addition, suitable strategies for performing multivariate design are presented and discussed. A practical case study is used to show the application of the techniques illustrated throughout the paper, and a preliminary rubble mound breakwater design is also carried out.