Smooth construction of impulse response functions and applied loads using a time domain deconvolution method

A time domain deconvolution method is developed to allow for continuous and differentiable impulse response function (IRF) constructions and applied force reconstructions. This is a two stage method where (1) the IRF is constructed using measured outputs and applied dynamic loads and (2) a dynamic applied load is reconstructed using measured outputs and the constructed IRF. A generalized formulation is presented which would allow for any assumed form of the unknown IRF. Subsequently, linear and cubic example cases are presented. The latter allows for continuous and differentiable solutions due to the ability to match time derivatives at each node. The problem of ill-conditioning in the deconvolution formulation is alleviated by assuming a distribution of the unknown IRF or applied force overmany sampling intervals where only the nodal values are of interest. This results in a matrix equation with many more rows than columns and is subsequently solved using a least squares pseudo inverse. The third order reconstructions are shown to more accurately reconstruct unknown IRF and applied load when the sampling rate is small or when the constraint parameters are large. The condition number is reduced for both the linear and cubic cases as the constraint parameters are increased, meaning both methods are effective at reducing ill-conditioning. (C) 2018 Elsevier Ltd. All rights reserved.