DINAME 2017 - Proceedings of the XVII International Symposium on Dynamic Problems of Mechanics A. T. Fleury, D. A. Rade, P. R. G. Kurka (Editors), ABCM, S˜ ao Sebasti ˜ ao, SP, Brazil, March 5-10, 2017 Operational modal analysis under wind load using stochastic sub- space identification Gustavo B. Wagner 1 , Damien Foiny 1 , Rubens Sampaio 1 , Roberta Lima 1 1 Pontif´ ıcia Universidade Cat ´ olica do Rio de Janeiro - Rua Marquˆ es de S˜ ao Vicente, 225, G´ avea - Rio de Janeiro, RJ - Brasil - 22451-900 , gustavo gbw@hotmail.com, damien.foiny@gmail.com, rsampaio@puc-rio.br, robertalima@puc- rio.br Abstract: The extraction of modal parameters from a real structure represents an important step in modal analysis. When only the output signal is available in an experiment, the system identification process is referred as operation modal analysis (OMA). Applications of those cases are fond for structures where the ambient excitation (wind, traffic, waves, nearby systems, etc.) can not be removed or is the only possible one. Once the input signals can not be measured, some assumptions in their random nature are needed together with a stochastic modeling of the system. Among several methods, the stochastic subspace identification (SSI) has been shown to be a consistent one and, therefore, was chosen to be used in this paper. Here, the modal analysis of a system under wind load is studied. The fluid-structure interaction force is usually not easy to be represented and its whiteness (assumption made in most of OMA methods) can not be easily conformed. In this way, a two floor building model is used for experimental validation, where different fluid- structure interaction were created. The paper begins with a presentation of the discrete state space model followed by the SSI theory. Two popular SSI algorithms are presented: covariance-driven and data-driven. A efficient way to select the correct parameters for the method is discussed together with a procedure to analyze the results. To exemplify the identification process, experimental results are shown and the identified parameters are listed. As conclusion, the wind has been shown to be a good excitation source for OMA once the system has been correct identified. Keywords: Operational modal analysis, System identification, Stochastic subspace methods, wind excitation, experi- mental validation INTRODUCTION Operational Modal Analysis (OMA) consist in find the dynamic characteristic of a structure through its modal param- eters using output-only signals. Differently from the classical approach of Experimental Modal Analysis (EMA), where the input signal are also measured, OMA only uses the stochastic nature of the inputs, assumed to be random due the ambient conditions. This fact allows system identification to be done under circumstances where EMA is limited, which includes: large and heavy structures, where a controlled input is hard and expensive, and identification process of systems under operational conditions, where interferences from the location can not be eliminated. With its majors developments happening in the early 1990s, applications of OMA in the structural dynamic field is far from reach its total potential. Nowadays, OMA has been used as tool in two main areas. The first is in the model vali- dation of big structures such as bridges, tall buildings, stadiums and oil rigs (Rainieri and Fabbrocino, 2014)(Rodrigues, 2004)(Brincker and Ventura, 2015). These structures have in common the heavy weight and the acting ambient forces. The excitation are done by wind, traffic, and waves which are difficult to model and measure. Therefore, OMA methods for parameters estimations suits very well in those cases (Reynders et al.,2015) (Reynders et al.,2008a). Recent articles have also focused on the variance estimation of the modal parameters. Mellinger et al.(2016), for example, measured the uncertainties in the modal parameter of a aircraft during in-flight tests. Other main application where OMA has been developed in the recent years is in the field of structural health monitoring (SHM)(Liu, 2011)(Farrar, 2013)(Deraemacker, 2010). It is done by a periodic modal identification, which evaluates a possible change in the modal parameters. Cracks, corrosion, unfastened bolts and etc. usually reduces the system stiffness modifying natural frequencies and mode shapes. The purpose of this article is to demonstrate a complete procedure of system identification in a real structure under wind load using stochastic subspace method. Becoming popular in the 2000s, stochastic subspace identification (SSI) consists in a collection of techniques that can be formulated in a consistent framework, where properties of the system can be estimated through matrix subspaces. The two principal subspace algorithms found in the literature are covariance- driven and data-driven, which consist in estimate the system controllability matrix using covariance matrices or orthogonal projections of the output signal. For a clear understanding of such methods, the extension of the state space model are done by the arrangement of the data in Hankel matrices. The methods performance heavily depends in the Hankel matrices dimension, since they are direct related to the number of elements in the estimation of covariances, the system order and the ratio between the interested frequency and the sampling frequency.