Multielement polynomial chaos Kriging-based metamodelling for Bayesian inference of non-smooth systems
Multielement polynomial chaos Kriging-based metamodelling for Bayesian inference of non-smooth systems
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DOI：
10.1016/j.apm.2022.11.039
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发表时间：
2022-12
期刊：
影响因子：
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通讯作者：
J. C. Garc'ia-Merino;C. Calvo-Jurado;E. Mart'inez-Paneda;E. Garc'ia-Mac'ias
中科院分区：
文献类型：
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作者：
J. C. Garc'ia-Merino;C. Calvo-Jurado;E. Mart'inez-Paneda;E. Garc'ia-Mac'ias
本文提出了一种基于区域划分的代理建模技术，用于高度非线性工程模型的贝叶斯参数推断。为了减轻贝叶斯推理应用中的计算负担，提出了一种基于多元多项式混沌展开的Kriging元模型。开发的代理模型结合在一个分段函数的一个数组的局部多项式混沌基于克里格元模型构建的随机输入空间的一组有限的非重叠子域。因此，存在的非平滑性的响应的正演模型（例如，非线性和稀疏性），可以再现所提出的元模型与最小的计算成本，由于其本地自适应能力。模型参数的推断是通过马尔可夫链蒙特卡罗方法，包括自适应探索和延迟拒绝。所提出的方法的效率和准确性进行了验证，通过两个案例研究，包括一个分析基准和数值的案例研究。后者涉及在热脱附光谱测试中控制金属材料的氢扩散现象的偏微分方程。
This paper presents a surrogate modelling technique based on domain partitioning for Bayesian parameter inference of highly nonlinear engineering models. In order to alleviate the computational burden typically involved in Bayesian inference applications, a multielement Polynomial Chaos Expansion based Kriging metamodel is proposed. The developed surrogate model combines in a piecewise function an array of local Polynomial Chaos based Kriging metamodels constructed on a finite set of non-overlapping subdomains of the stochastic input space. Therewith, the presence of non-smoothness in the response of the forward model (e.g. nonlinearities and sparseness) can be reproduced by the proposed metamodel with minimum computational costs owing to its local adaptation capabilities. The model parameter inference is conducted through a Markov chain Monte Carlo approach comprising adaptive exploration and delayed rejection. The efficiency and accuracy of the proposed approach are validated through two case studies, including an analytical benchmark and a numerical case study. The latter relates the partial differential equation governing the hydrogen diffusion phenomenon of metallic materials in Thermal Desorption Spectroscopy tests.