Identification of random variation in structures and their parameter estimates

Structures that are members of an ensemble of nominally identical systems actually differ due to variations in details among individuals. Furthermore, there are variations in the system response of an individual structure that can be attributed to unmeasured conditions (such as temperature and humidity) that are present during experiments. Finally, noise is present in all measurements of structural excitations and responses. For these reasons, there is always random variation associated with the characterizations of structural dynamic systems, and descriptions of results must be in statistical or probabilistic terms. This study identifies and assesses the sources and the degrees of randomness in a metric of structural dynamics of a given system through experiments and analysis. Nomenclature h = an n x 1 vector random source of Impulse Response Practically all physical structures are subjected to dynamic environments. The dynamic response of some structures governs their design and therefore, characterizing the dynamic behavior of structures is important. However, the dynamic characteristics of physical structures that are nominally identical exhibit random variation (see Paez, Hunter, and Cafeo, 2002 [5], [6]). Specifically, manufacturing processes that seek to produce identical systems fail to do so because the equipment used to fabricate parts and the procedures used to construct components and systems are imperfect. The small variations in hardware and fabrication procedures yield systems with differing vibration characteristics. Function realizations hi = an IRF realization of vector random source h q = structural excitatio