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Novel parameter update for a gradient based MCMC method for solid-void interface detection through elastodynamic inversion
Probabilistic Engineering Mechanics ( IF 2.6 ) Pub Date : 2020-10-01 , DOI: 10.1016/j.probengmech.2020.103097
Michael Conrad Koch , Kazunori Fujisawa , Akira Murakami

Abstract A method is developed for the explicit identification of solid-void interfaces in a Bayesian framework using a statistically efficient gradient based Markov Chain Monte Carlo (MCMC) algorithm called Hamiltonian Monte Carlo (HMC). The elastodynamic inversion is carried out in a Finite Element discretized domain considering parameterized representations of the actual interface between the elastic solid and void embedded in the solid itself. Using a reference configuration, a parameter update procedure is designed, to ensure reversibility of the HMC algorithm, thereby satisfying the detailed balance condition. The quality of mesh at every parameter update is maintained through a simple mesh moving strategy that introduces volume scaled Elastic modulus in the mesh moving stage. HMC gradient computation procedure is detailed for a general parameterization of the interface. Integration of these techniques with the HMC algorithm enables the continuous variation of parameters and maintains continuity of the Hamiltonian. The performance of the proposed method is investigated with respect to two solid-void interface identification problems, one of well-defined and the other of arbitrary geometry. Results show that the proposed method performs well, maintaining a good mesh quality after each parameter update. The Markov chains converge and statistical descriptions of the inferred parameters are obtained.

中文翻译:

基于梯度的 MCMC 方法通过弹性动力学反演进行固体-空隙界面检测的新参数更新

摘要 开发了一种使用称为哈密顿蒙特卡罗 (HMC) 的基于统计有效梯度的马尔可夫链蒙特卡罗 (MCMC) 算法在贝叶斯框架中显式识别固体-空隙界面的方法。考虑到弹性固体和嵌入固体本身的空隙之间的实际界面的参数化表示,在有限元离散域中进行弹性动力学反演。使用参考配置,设计参数更新程序,保证HMC算法的可逆性,从而满足详细的平衡条件。通过在网格移动阶段引入体积缩放弹性模量的简单网格移动策略来保持每次参数更新时的网格质量。HMC 梯度计算过程详细介绍了接口的一般参数化。这些技术与 HMC 算法的集成使参数能够连续变化并保持哈密顿量的连续性。对所提出的方法的性能进行了研究,该问题涉及两个固体-空隙界面识别问题,一个是明确定义的,另一个是任意几何形状的。结果表明,所提出的方法性能良好,在每次参数更新后都能保持良好的网格质量。马尔可夫链收敛并获得推断参数的统计描述。对所提出的方法的性能进行了研究,该问题涉及两个固体-空隙界面识别问题,一个是明确定义的,另一个是任意几何形状的。结果表明,所提出的方法性能良好,在每次参数更新后都能保持良好的网格质量。马尔可夫链收敛并获得推断参数的统计描述。对所提出的方法的性能进行了研究,该问题涉及两个固体-空隙界面识别问题,一个是明确定义的,另一个是任意几何形状的。结果表明,所提出的方法性能良好,在每次参数更新后都能保持良好的网格质量。马尔可夫链收敛并获得推断参数的统计描述。
更新日期:2020-10-01
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