Introduction

In Chapter 1 it is mentioned that a dynamic analysis can be carried out in two different ways, depending on how the loads are described. One alternative is a deterministic analysis, which requires that the load time history is fully known. The other alternative is a stochastic analysis, where statistical concepts are used to specify the loads. In this chapter we show why (and how) it is expedient and necessary to use statistical and probabilistic methods to describe a number of load types to which structures are subjected.

Typical examples are wind loads on a high-rise building or a suspension bridge, wave loads on an offshore structure or a floating bridge. When the loads on a structure are described in terms of statistical quantities, then the response must also be described and analyzed in terms of the same kind of quantities.

Examples of Stochastic Modeling

Atypical feature of a series of physical phenomena of engineering interest is that each one of them under seemingly identical conditions exhibit quite different behaviour from one recorded experiment to the next. In addition, each recorded time history of the quantity studied is often characterized by being highly irregular.

Figure 5.1 shows three time histories of the water surface elevation measured in a laboratory wave tank. This tank is equipped with a wave maker that can be used to generate irregular waves similar to those observed on the open ocean. The three recorded wave elevations represent the same wave condition, and the three time histories do look quite similar when the overall picture is considered. However, to mimic reality the waves were generated in such a way that when the three time series are subjected to closer scrutiny, it is seen that there are significant differences between them on a local level. Another salient feature of these time histories is that they look irregular or random, as do real waves.