ABSTRACT

A large number of phenomena in science and engineering either defy any attempt of a deterministic description or only lend themselves to a deterministic description at the price of enormous difficulties. Examples of such phenomena are not hard to find: the height of waves in a rough sea, the noise from a jet engine, the electrical noise of an electronic component or, if we remain within the field of vibrations, the vibrations of an aeroplane flying in a patch of atmospheric turbulence, the vibrations of a car travelling on a rough road or the response of a building to earthquake and wind loads. Without doubt, the question as to whether any of the above or similar phenomena is intrinsically deterministic and, because of their complexity, we are simply incapable of a deterministic description is legitimate, but the fact remains that we have no way to predict an exact value at a future instant of time, no matter how many records we take or observations we make. However, it is also a fact that repeated observations of these and similar phenomena show that they exhibit certain patterns and regularities that fit into a probabilistic description. This occurrence suggests taking a different and more pragmatic approach, which has turned out to be successful in a large number of practical situations: we simply leave open the question about the intrinsic nature of these phenomena and, for all practical purposes, tackle the problem by defining them as ‘random’ and adopting a description in terms of probabilistic statements and statistical averages.