Input Force Reconstruction Using a Time Domain Technique

A time domain method is presented for estimating the discrete input forces acting on a structure based upon its measured response. The structure is essentially transformed into its own loads transducer. A set of inverse system Markov parameters, in which the roles of input and output are reversed, is estimated from forward system Markov parameters using a linear predictive scheme. Inputs and acceleration outputs are assumed to be collocated to maintain minimum phase. Subsequently, any set of measured operational sensor data of any time duration can be convolved with the inverse Markov parameters to produce estimates of the input forces. This problem is ill-posed, so a regularization technique is employed to stabilize computations. A stability analysis is performed to illustrate the effects of the regularization. Predicted pseudo-forces qualitatively approximate the actual input forces and, when applied back to the structure, produce accelerations which accurately match the measured operational sensor data.