Joint input-response estimation for structural systems based on reduced-order models and vibration data from a limited number of sensors

An algorithm is presented for jointly estimating the input and state of a structure from a limited number of acceleration measurements. The algorithm extends an existing joint input-state estimation filter, derived using linear minimum-variance unbiased estimation, to applications in structural dynamics. The filter has the structure of a Kalman filter, except that the true value of the input is replaced by an optimal estimate. No prior information on the dynamic evolution of the input forces is assumed and no regularization is required, permitting online application. The effectiveness and accuracy of the proposed algorithm are demonstrated using data from a numerical cantilever beam example as well as a laboratory experiment on an instrumented steel beam and an in situ experiment on a footbridge.