Derivation of statistical properties of wave-induced offshore structural response by principal component technique

Abstract

According to linear random wave theory, water particle kinematics at different nodes of an offshore structure form a set of correlated jointly Gaussian random variables. Thus, using principal component analysis, all the foregoing kinematics can be expressed as linear combinations of a few independent Gaussian random variables. This technique can be used to generate statistically independent hydrodynamic load and response values, as opposed to time simulation technique that leads to correlated response values. The sampling variability of the statistics generated from a set of independent data points is considerably smaller than that of a set (of the same size) of correlated values. Therefore, a much smaller number of simulated data points are necessary for accurate prediction of the statistical properties of response. Furthermore, simulating N data points by principal component technique (PCT) has proved to be at least two times faster than simulating the same number of data points by the time simulation technique (TST). As a result, PCT is considerably more efficient (about 25 times) than TST. The forgoing conclusions have been verified by applying both techniques to two test structures under different environmental conditions.