Reference-based Stochastic Subspace Identification for Output-only Modal Analysis

When performing vibration tests on civil engineering structures, it is often unpractical and expensive to use arti"cial excitation (shakers, drop weights). Ambient excitation on the contrary is freely available (tra$c, wind), but it causes other challenges. The ambient input remains unknown and the system identi"cation algorithms have to deal with output-only measurements. For instance, realisation algorithms can be used: originally formulated for impulse responses they were easily extended to output covariances. More recently, datadriven stochastic subspace algorithms which avoid the computation of the output covariances were developed. The key element of these algorithms is the projection of the row space of the future outputs into the row space of the past outputs. Also typical for ambient testing of large structures is that not all degrees of freedom can be measured at once but that they are divided into several set-ups with overlapping reference sensors. These reference sensors are needed to obtain global mode shapes. In this paper, a novel approach of stochastic subspace identi"cation is presented that incorporates the idea of the reference sensors already in the identi"cation step: the row space of future outputs is projected into the row space of past reference outputs. The algorithm is validated with real vibration data from a steel mast excited by wind load. The price paid for the important gain concerning computational e$ciency in the new approach is that the prediction errors for the non-reference channels are higher. The estimates of the eigenfrequencies and damping ratios do not su!er from this fact. ( 1999 Academic Press