Statistical Theory of the Vector Random Decrement Technique

The Vector Random Decrement technique has previously been introduced as an effcient method to transform ambient responses of linear structures into Vector Random Decrement functions which are equivalent to free decays of the current structure. The modal parameters can be extracted from the free decays. Due to the speed and/or accuracy of the Vector Random Decrement technique, it was introduced as an attractive alternative to the Random Decrement technique. In this paper, the theory of the Vector Random Decrement technique is extended by applying a statistical description of the stochastic processes describing the ambient measurements. The Vector Random Decrement functions are linked to the correlation functions of the stochastic processes provided they are stationary and Gaussian distributed. Furthermore, a new approach for quality assessment of the Vector Random Decrement functions is given on the basis of the derived results. The work presented in this paper makes the theory of the Vector Random Decrement technique equivalent to the theory of the Random Decrement technique. The theoretical derivations are illustrated by the analysis of the response of a 3DOF system loaded by white noise.