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- Title
Efficient evaluation of small failure probability in high-dimensional groundwater contaminant transport modeling via a two-stage Monte Carlo method.
- Authors
Zhang, Jiangjiang; Li, Weixuan; Lin, Guang; Zeng, Lingzao; Wu, Laosheng
- Abstract
In decision-making for groundwater management and contamination remediation, it is important to accurately evaluate the probability of the occurrence of a failure event. For small failure probability analysis, a large number of model evaluations are needed in the Monte Carlo (MC) simulation, which is impractical for CPU-demanding models. One approach to alleviate the computational cost caused by the model evaluations is to construct a computationally inexpensive surrogate model instead. However, using a surrogate approximation can cause an extra error in the failure probability analysis. Moreover, constructing accurate surrogates is challenging for high-dimensional models, i.e., models containing many uncertain input parameters. To address these issues, we propose an efficient two-stage MC approach for small failure probability analysis in high-dimensional groundwater contaminant transport modeling. In the first stage, a low-dimensional representation of the original high-dimensional model is sought with Karhunen-Loève expansion and sliced inverse regression jointly, which allows for the easy construction of a surrogate with polynomial chaos expansion. Then a surrogate-based MC simulation is implemented. In the second stage, the small number of samples that are close to the failure boundary are re-evaluated with the original model, which corrects the bias introduced by the surrogate approximation. The proposed approach is tested with a numerical case study and is shown to be 100 times faster than the traditional MC approach in achieving the same level of estimation accuracy.
- Subjects
GROUNDWATER management; MOVEMENT of solutes in soils; MONTE Carlo method
- Publication
Water Resources Research, 2017, Vol 53, Issue 3, p1948
- ISSN
0043-1397
- Publication type
Article
- DOI
10.1002/2016WR019518