Load Reconstruction Technique Using D-Optimal Design and Markov Parameters

This paper develops a technique for identifying dynamic loads acting on a structure based on impulse response of the structure, also referred to as the system Markov parameters, and structure response measured at optimally placed sensors on the structure. Inverse Markov parameters are computed from the forward Markov parameters using a linear prediction algorithm and have the roles of input and output reversed. The applied loads are then reconstructed by convolving the inverse Markov parameters with the system response to the loads measured at optimal locations on the structure. The structure essentially acts as its own load transducer. It has been noted that the computation of inverse Markov parameters, like most other inverse problems, is ill-conditioned which causes their convolution with the measured response to become quite sensitive to errors in system modeling and response measurements. The computation of inverse Markov parameters (and thereby the quality of load estimates) depends on the locations of sensors on the structure. To ensure that the computation of inverse Markov parameters is well-conditioned, a solution approach, based on the construction of D-optimal designs, is presented to determine the optimal sensor locations such that precise load estimates are obtained.