Input loading on certain mechanical and structural systems, such as earthquake loading on building structures, ocean waves acting on offshore platforms and turbulent air flow on aircraft wings, may be treated as random input to these systems and usually is difficult to measure. A technique, called the Random Decrement Technique, has been applied to extract system modal parameters from measured system responses without any knowledge of the applied random excitation forces. Although the technique has been widely applied in many engineering problems, it has not, been fully resized due to its tack of a solid mathematical foundation. A straight forward analytical approach using the governing equation.3 of motion is presented in this paper to measles the mathematical foundation of the Random Decrement Technique for general multi-degree-of-freedom linear systems subjected to stationary input, and to prove that the signatures produced by the Random Decrement Process are requirement to the free decay responses of the systems. The initial conditions of these signatures are quantitatively discussed, and an example is included to demonstrate the reliability of this technique.
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