Dynamic loads identification in presence of unknown but bounded measurement errors

In this paper, a time-domain inverse method that combines the set membership identification theory with interval analysis is proposed to stably identify structural dynamic loads, in which circumstances the unknown-but-bounded (UBB) uncertainty in measured responses is considered. Instead of knowing precise statistical information, the noisy responses are treated as intervals, and hence only their bounds are needed. The procedure of dynamic loads reconstruction from noisy displacement measurements is mainly studied, and the correlation between the uncertain responses of displacement and acceleration is also investigated in order to deal with the practical problems effectively, where only uncertainty information of acceleration can be known. Moreover, for purpose of comparison, the traditional Green’s function method is introduced and further applied into engineering simulations (a ten-bar plane truss and a twenty-five-bar space truss). A test example of a four-story frame structure is eventually presented with limited acceleration sample data. The identified results of the three examples above illustrate the feasibility and accuracy of the developed method.