Abstract 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 l1 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.

中文翻译：

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用于快速自适应力重建的逐元素贝叶斯正则化

摘要 在时域力重建问题中，正则化技术被广泛采用来解决固有的不适定性或病态。为具有不同时间分布的力选择不同的技术，例如平滑力的 Tikhonov 正则化和稀疏力的 l1 正则化。然而，由于缺乏关于力时间分布的先验信息，选择合适的正则化技术很麻烦。在本文中，我们提出了一种新的正则化技术，可以在已知位置重建具有不同类型时间分布的力。所提出的方法，称为逐元素贝叶斯正则化，是在分层贝叶斯框架下制定的，假设未知力历史中的每个元素都有一个单独的先验分布。通过力历史的后验概率的条件最大化，为每个单独的元素自动和自适应地设置适当的正则化级别。所提出的方法通过悬臂板模拟、工程规模坦克模拟和不同噪声水平和力类型下的实验室坦克实验进行了验证。结果表明，所提出的方法可以在各种条件下以快速的计算速度准确地重建力历史，而无需任何先验信息。所提出的工作主要关注单输入多输出情况，但所提出的方法可以很容易地扩展到多输入多输出情况。