Traditional time domain force identification methods require prior knowledge about the force profile to apply the appropriate regularization term. Generally speaking, ℓ1 and ℓ2 regularization are applied for sparse-type and continuous-type forces respectively. However, prior knowledge about the force type may be unavailable in engineering practice. It is then necessary to incorporate the determination of q (as in ℓq regularization) into the identification process. In this paper, we propose two methods to address the problem: the joint and marginal posterior modes of the force history. The identification problem is formulated within the Bayesian framework. The force history, precision parameters, and q are all treated as unknown random parameters, and estimated based on vibration measurements only. The proposed methods are numerically validated on a mass–spring system, an engineering-scale support structure and experimentally validated on a cantilever beam. It is shown that the proposed methods by considering the data-driven determination of q could adapt to the force profile and consistently provide satisfactory results.
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