Finite-Simulation Error Bounds for Estimated K-Year Forces

Abstract

Computer simulations have been used frequently to calculate design loads associated with a specific return period for offshore structures. However, two important questions persistently confront engineers who simulate load events on computers to estimate k -year forces: 1) How accurate is the estimated k -year force (say, 100-yr force) obtained through a computer simulation of n years (e.g., n = 1000) compared to that which would result from a much longer simulation? 2) When can we stop a computer simulation? Or how many simulation years are needed to reach a specified level of reliability for a certain k -year force? This paper presents solutions to these two questions under the assumption that the input parameters are completely known and the formulas used to compute loads are one hundred percent correct. Given a confidence level C (e.g., C = 80 or 90 percent) and an arbitrary but fixed number of simulation years, a method is identified to find an estimated k -year force and an error bound α, such that Pr(|estimator−k-year force|<α)>C (1) In addition, when the required confidence C and error bound α are given, a procedure is given to stop a computer simulation as soon as inequality (1) is satisfied. These results are not dependent on the statistical distribution of the underlying force distribution. Therefore, one does not have to assume that forces are of a specific probability distribution (such as lognormal, exponential, etc.).