By M. A. Perry
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Extra info for Aerospace Instrumentation. Proceedings of the Fourth International Aerospace Symposium
Reference 1. CRANDELL, S. H . and MARKS, W . D . Random Vibration in Mechanical Systems, A NEW METHOD FOR ANALYSING RANDOM PROCESSES G. COUPRY Office National d'Etudes et de Recherches Aérospatiales Introduction During the past three years, the Department of Structures at O N E R A has been interested in the response of flexible airplanes to flight turbulence, and numerous flight tests have been performed. At the beginning, nearly all the standard methods for reducing random processes—with all their qualities and shortcomings—were used for the analysis of the flight data.
In the opinion of the authors the field of study of r a n d o m processes is one in which the theoretical developments have outstripped the field of engineering interpretation. In short, whilst there are many mathematical techniques available, and sophisticated analysers for data processing, the most significant area of ignorance is in the interpretation of the information gained to improving designs, if it is a develop ment project, or to improving our basic knowledge if it is a research project.
This is in fact the result of the important Wiener-Khitchine theorem, that the autocorrelation function and the power spectrum are Fourier transform pairs. This point is of importance in digital analysis, discussed below. It may be noted that there is a loss of information in forming an autocorrela tion function from a time function; all phase information is lost (as it also is, of course, when a power spectrum is formed). It is also easily shown that an autocorrelation function is symmetrical about zero delay, and has its maximum value at zero delay.