Research on interval identification method for dynamic loads based on Green's function

Based on the time series of the displacement responses, an interval analysis method has been proposed to identify the time history of the dynamic loads of structures. The dynamic loads were expressed as a series of pulse response functions in time domain, and the structural dynamic response was the convolution integral of the loads and the corresponding unit-pulse response function(Green's function). The time series of the uncertain-but-bounded displacement responses were quantified by the interval vectors, and the Green's function was discretized to obtain the interval linear equations. The interval estimations of the loads could be obtained by solving the interval linear equations by the interval perturbation method. Furthermore, a more accurately estimated interval was obtained by the membership-set operations on the identified loads intervals corresponding to the displacements of different receiving points. In the end, a 10-bars truss structure and a cantilever beam structure were used to illustrate the effectiveness and applicability of the presented method.