Numerical methods for calculating the crossing rate of high and extreme response levels of compliant offshore structures subjected to random waves

The focus of the paper is on methods for calculating the mean upcrossing rate of stationary stochastic processes that can be represented as second order stochastic Volterra series. This is the current state-of-the-art representation of the horizontal motion response of e.g. a tension leg platform in random seas. Until recently, there has been no method available for accurately calculating the mean level upcrossing rate of such response processes. Since the mean upcrossing rate is a key parameter for estimating the large and extreme responses it is clearly of importance to develop methods for its calculation. The paper describes in some detail a numerical method for calculating the mean level upcrossing rate of a stochastic response process of the type considered. Since no approximations are made, the only source of inaccuracy is in the numerical calculation, which can be controlled. In addition to this exact method, two approximate methods are also discussed.