AN INPUT/OUTPUT-BASED PROCEDURE FOR FULLY EVALUATING AND MONITORING DYNAMIC PROPERTIES OF STRUCTURAL SYSTEMS VIA A SUBSPACE IDENTIFICATION METHOD

Dynamic behaviour of complex structural systems may be modelled by a system of second order linear ordinary differential equations, i.e., Mẅ(t)+Dẇ(t)+Sw (t)=f (t), by means of either structural analysis for finite degree-of-freedom systems or discretization procedures (e.g., FE methods) for continuous systems. Here, w (t) and f (t) are the displacement vector and the force vector. Owing to erosion, friction, and internal damage and cracks, etc., a working process of a system always accompanies gradual degradation of the performance of this system: the stiffness of the system weakens, whereas the damping of the system strengthens. To evaluate such degradation, the usual way is to model the evolution of property of a system, obtain system property parameters, trace the history of motion and loading, carry out complicated analysis and computation under prescribed initial and boundary value conditions, and finally derive the degraded property and responses of the system. This traditional way, however, might be cumbersome and unsatisfactory in some cases due to the lack of adequate experimental data and well-founded theoretical basis, etc. Another way is to apply “inverse” methods, such as modal analysis methods with FFT and a subspace identification method, etc., developed in the theory of system identification, which extracts information about system properties directly from experimental input/output measurement data and hence do not involve the foregoing traditional analysis. The latter method, however, could not supply full information about system properties due to the assumption of the “black box” viewpoint. In this work, with suitable experimental input/output measurement data, a simple, effective procedure is described by which the stiffness matrix S and the damping matrix D may be determined in a complete, unique manner using a subspace identification method. The possibility of such a procedure arises from the observation of the self-evident fact: the conservation of mass of any part of a structural system implies that the mass matrix M of this system is constant and hence is given by its initial value. The stiffness and damping matrices S and D determined by the proposed procedure may be used to evaluate and monitor, in a full sense, the degradation of dynamic properties of structural systems. Further, with the information about the stiffness distribution of constituent elements of a structural system it is shown that it may be possible to estimate the locations of the damaged or faulty elements in this system. An example is given to illustrate the application of the proposed procedure.