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.
翻译:本文介绍了一种基于对高非线性工程模型进行高度非线性工程模型参数推断的域隔替代模型技术。为了减轻贝叶西亚推论应用中通常涉及的计算负担,提议了一种基于克里吉的多元素多元混乱扩展元模型。开发的代孕模型将一系列基于局部多元混乱的当地多部混乱元模型以小片功能组合在一起,这些模型以一组非重叠的有限分域结构构建在蒸汽输入空间中,其效率与准确性通过两个案例研究得到验证,包括分析基准和数字案例研究,后者涉及前方模型反应中的非移动性(例如~非线性和稀少性),其当地适应能力导致最低计算成本。模型参数通过Markov 链 Monte Carlo 方法进行,其中包括适应性探索和延迟拒绝。拟议方法的效率和准确性通过两个案例研究,包括分析基准和数字案例研究得到验证。后者涉及在Thesmal Declogiscommexpractal测试中对金属材料氢扩散现象进行部分差异方程式的公式。