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Element-wise Bayesian regularization for fast and adaptive force reconstruction
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DOI：10.1016/j.jsv.2020.115713.png)
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Abstract
En 中文
In time domain force reconstruction problems, regularization techniques are widely adopted to solve the intrinsic ill-posedness or ill-conditioning. Different techniques are selected for forces with different temporal profiles, such as Tikhonov regularization for smooth forces and l(1) regularization for sparse forces. However, in lack of prior information on force temporal distribution, choosing the appropriate regularization technique is troublesome. In this paper, we propose a novel regularization technique that can reconstruct forces with different types of temporal profiles at known locations. The proposed method, named Element-wise Bayesian regularization, is formulated under the hierarchical Bayesian framework, with an individual prior distribution assumed for each element in the unknown force history. An appropriate regularization level is automatically and adaptively set for each individual element through conditional maximization of the posterior probability of force history. The proposed method is validated by a cantilever plate simulation, an engineering-scale tank simulation, and a laboratory tank experiment under different noise levels and force types. The results conclude that the proposed method accurately reconstruct force histories without any prior information at a fast computation speed under various conditions. The presented work primarily focuses on the single input multiple output case, but the presented methodology can be easily extended towards the multiple input multiple output case. (C) 2020 Elsevier Ltd. All rights reserved.
Keywords:
Inverse problem
Force identification
Force reconstruction
Bayesian regularization
Conditional maximization
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