Bayesian calibration of multi-response systems via multivariate Kriging: Methodology and geological and geotechnical case studies
Bayesian calibration of multi-response systems via multivariate Kriging: Methodology and geological and geotechnical case studies
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DOI：
10.1016/j.enggeo.2019.105248
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发表时间：
2019-10
影响因子：
7.4
通讯作者：
M. Rahimi;A. Shafieezadeh;Dylan Wood;E. Kubatko;N. Dormady
中科院分区：
文献类型：
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作者：
M. Rahimi;A. Shafieezadeh;Dylan Wood;E. Kubatko;N. Dormady
贝叶斯技术——广泛用于根据在空间和时间不同点的新观测来更新所涉及的不确定系统变量的分布——在复杂的计算模型的情况下可能要求很高，而且令人望而却步。在此，我们提出了一个高效的贝叶斯更新框架，该框架结合多元Kriging代理模型来量化不确定系统变量整个空间中的异方差不确定性，并利用不可分协方差结构捕获响应之间的时空依赖关系。三个地质和岩土工程实例证明了所提出框架的优势，因为地质性质通常是高度不确定的，并且这些系统的响应通常是多元的。结果表明，与现有的基于代理模型的贝叶斯更新方法相比，所开发的框架能够准确有效地更新系统变量的不确定性。此外，考虑到经常被忽视的响应之间的时空依赖关系，可以显著提高预测的准确性。所提出的方法是一种有效的工具，可以最佳地利用地质和岩土工程系统的监测数据，从而对未来的响应进行可靠的预测。
Bayesian techniques – widely used to update the distributions of involved uncertain system variables based on new observations at different points in space and time – can be highly demanding and prohibitive in cases of sophisticated computational models. Here, we propose a highly efficient Bayesian updating framework that is integrated with multivariate Kriging surrogate modeling to quantify heteroscedastic uncertainties in the entire space of uncertain system variables and capture spatial and temporal dependencies among the responses using non-separable covariance structure. The advantages of the proposed framework are demonstrated on three geological and geotechnical examples, since geological properties are often highly uncertain and responses in these systems are frequently multivariate in nature. Results indicate that the developed framework is able to accurately and efficiently update uncertainties of system variables compared to existing Bayesian updating methods that are based on surrogate models. Moreover, considering the often-neglected spatiotemporal dependencies between responses is observed to noticeably enhance the accuracy of predictions. The proposed approach serves as an efficient tool to optimally utilize monitoring data from geological and geotechnical systems to arrive at reliable predictions of future responses.