Chapter11 Structural Identification Using Response Measurements Under Base Excitation Suparno Mukhopadhyay, Raimondo Betti, and Hilmi Lus¸ Abstract In vibration-based structural identification, experimentally obtained modal parameters from measured structural responses are often used, along with some information about the structural model, for identifying the physical parameters, i.e. mass and stiffness matrices of the structural system. In this study, we consider this problem of physical parameter identification for building structures subjected to base excitation, and attempt to address the issues of (a) unknown scaling of experimental mode shapes, (b) incomplete instrumentation, and (c) incomplete information of the physical parameters of the structural system prior to identification. A mode shape normalization and expansion approach, which incorporates the information available from the structural topology of the physical system in terms of its modal parameters, is discussed. Using this proposed approach, along with the modal orthogonality relations, the mass and stiffness matrices of the system can be estimated. The performance of the algorithm is finally evaluated through numerical simulations of base acceleration induced vibrations of a 4-story shear-type frame, as well as using experimental data collected from a 4-story frame subjected to base excitation on a shake table facility. The use of the modal-and-physical parameter identification method for the purpose of structural damage detection is also investigated using the experimental data, with the damage being represented by a reduction in the cross-sectional area of two columns of the “healthy” frame. Keywords Structural identification • Incomplete instrumentation • Incomplete a priori information • Mass normalization • Mode shape expansion 11.1 Introduction As evidenced by the extensive literature in experimental and operational modal analysis, the natural frequencies and mode shapes of a structural system may be obtained using measured responses from the actual system, subjected to operational or well-defined experimental excitations, by employing various system identification techniques [1]. These experimentally obtained modal parameters may then be used for identifying the physical parameters, e.g. the mass and stiffness matrices, of the structural system, thereby providing the engineer with a reliable model representing the structure’s current condition. This calibrated model can be used in increasing the reliability of structural analysis exercises, as well as, the variations in the model parameters that may be obtained from successive identifications can be used for structural health monitoring purposes through timely identification of possible structural damage. In practical implementations of the above scheme of structural parameter identification, one usually encounters different types of incompleteness in available information. One type of incompleteness results from limited instrumentation of the structural system, since it is usually infeasible to instrument all the degrees of freedom (DOF) defined in an analytical model of the system. Since, in such a situation, the experimental mode shape estimates are initially available only at the measured DOFs, an expansion of these incomplete mode shapes from the observed to the unobserved DOFs often emerges as a prerequisite to the physical parameter identification exercise. Moreover, for base acceleration induced vibration, the S. Mukhopadhyay ( ) •R. Betti Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA e-mail: sm3315@columbia.edu H. Lus¸ Department of Civil Engineering, Bogazici University, Bebek 34342, Istanbul, Turkey H.S. Atamturktur et al. (eds.), Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-04552-8__11, © The Society for Experimental Mechanics, Inc. 2014 107
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