Time domain force localization and reconstruction based on hierarchical Bayesian method

Abstract In engineering practice, localization and reconstruction of external excitations is a tough problem in absence of prior knowledge. Traditional regularization approaches require assigning regularization parameters and shape parameters before implementing the reconstruction. However, a poor selection of these parameters generally leads to a poor reconstruction. In this paper a time domain hierarchical Bayesian method is proposed to locate and reconstruct the external excitations with automatic selection of parameters. The entire method is performed in two stages. First based on the property of posterior probability distribution function of shape parameters, a novel non-force criterion is proposed to determine the non-force locations quickly. Then based on the determined force locations, a reduced-dimension problem is constructed and the posterior distributions of parameters are sampled by a Metropolis-within-Gibbs sampler with nested blocking technique. Both numerical simulations and laboratory experiment of a cantilever beam under various load conditions are carried out to validate the proposed method.