Time domain force identification based on adaptive ℓq regularization

Abstract

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.