In this paper, relationships between wave characteristics and upcrossing- and oscillation-intensities are used to construct conservative bounds for significant wave heights and amplitudes and for moments of waves crests and troughs. A concept of oscillation filtering is introduced for removing small waves. Results are illustrated by five examples in which both Gaussian and non-Gaussian models for a sea or a load are considered.
Let x(t) be the height of the sea level at a fixed point as a function of time t. In oceanographic applications x(t) is often seen as a sequence of waves where each wave can be described by means of its highest and lowest values (crest, trough), or by means of its amplitude (= crest - trough) and wave period, describing the duration of a single wave. There is no general agreement about the formal definition of a wave. Often one uses the so called mean downcrossing wave, where the wave is considered as a part of a function between the consecutive downcrossings of the mean sea level, (see the following definition). A simple measure of severity of waves are the significant wave amplitude and the significant crest height, denoted by H s, Ms, averages of the highest one-third of amplitudes H*, crests heights Mi*, respectively. A more complete statistical characteristic of waves are (crest, trough)- and (wave period, amplitude)- distributions. Two major uses of wave characteristic distributions are to predict extreme waves and fatigue lifetimes of marine structures. Clearly, using the mean crossing waves one neglects small oscillations superimposed on major waves. However, for fatigue accumulation in marine structures, it is well known that even small oscillations can contribute to the damage and hence have to be analyzed.
