skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Efficient evaluation of small failure probability in high-dimensional groundwater contaminant transport modeling via a two-stage Monte Carlo method: FAILURE PROBABILITY

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 testedmore » 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.« less

Authors:
ORCiD logo [1]; ORCiD logo [2];  [3]; ORCiD logo [1]; ORCiD logo [4]
  1. Zhejiang Provincial Key Laboratory of Agricultural Resources and Environment, Institute of Soil and Water Resources and Environmental Science, College of Environmental and Resource Sciences, Zhejiang University, Hangzhou China
  2. Pacific Northwest National Laboratory, Richland Washington USA
  3. Department of Mathematics and School of Mechanical Engineering, Purdue University, West Lafayette Indiana USA
  4. Department of Environmental Sciences, University of California, Riverside California USA
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1356505
Report Number(s):
PNNL-SA-122101
Journal ID: ISSN 0043-1397
DOE Contract Number:
AC05-76RL01830
Resource Type:
Journal Article
Resource Relation:
Journal Name: Water Resources Research; Journal Volume: 53; Journal Issue: 3
Country of Publication:
United States
Language:
English

Citation Formats

Zhang, Jiangjiang, Li, Weixuan, Lin, Guang, Zeng, Lingzao, and Wu, Laosheng. Efficient evaluation of small failure probability in high-dimensional groundwater contaminant transport modeling via a two-stage Monte Carlo method: FAILURE PROBABILITY. United States: N. p., 2017. Web. doi:10.1002/2016WR019518.
Zhang, Jiangjiang, Li, Weixuan, Lin, Guang, Zeng, Lingzao, & Wu, Laosheng. Efficient evaluation of small failure probability in high-dimensional groundwater contaminant transport modeling via a two-stage Monte Carlo method: FAILURE PROBABILITY. United States. doi:10.1002/2016WR019518.
Zhang, Jiangjiang, Li, Weixuan, Lin, Guang, Zeng, Lingzao, and Wu, Laosheng. Wed . "Efficient evaluation of small failure probability in high-dimensional groundwater contaminant transport modeling via a two-stage Monte Carlo method: FAILURE PROBABILITY". United States. doi:10.1002/2016WR019518.
@article{osti_1356505,
title = {Efficient evaluation of small failure probability in high-dimensional groundwater contaminant transport modeling via a two-stage Monte Carlo method: FAILURE PROBABILITY},
author = {Zhang, Jiangjiang and Li, Weixuan and Lin, Guang and Zeng, Lingzao and Wu, Laosheng},
abstractNote = {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.},
doi = {10.1002/2016WR019518},
journal = {Water Resources Research},
number = 3,
volume = 53,
place = {United States},
year = {Wed Mar 01 00:00:00 EST 2017},
month = {Wed Mar 01 00:00:00 EST 2017}
}
  • A methodology for modeling, in two dimensions, the transport of dissolved constituents in steady groundwater flow is presented. The model aims at the efficient confrontation of the difficulties associated with advection-dominated conditions (oscillation-free resolution of sharp fronts). Employing a spatial splitting algorithm within the framework of the (curvilinear) principal directions of transport formulation, it computes transport along streamlines by a variant of the pseudoviscosity method. The algorithm is subject to mild grid design constraints that afford efficiency in terms of CPU time and storage; its accuracy is tested against analytical solutions. The model is also applied to the simulation ofmore » the chloride plume observed under the Borden landfill in Ontario, Canada. Model calibration issues are discussed.« less
  • A calibrated groundwater flow model for a contaminated site can provide substantial information for assessing and improving hydraulic measures implemented for remediation. A three-dimensional transient groundwater flow model was developed for a contaminated mountainous site, at which interim corrective measures were initiated to limit further spreading of contaminants. This flow model accounts for complex geologic units that vary considerably in thickness, slope, and hydrogeologic properties, as well as large seasonal fluctuations of the groundwater table and flow rates. Other significant factors are local recharge from leaking underground storm drains and recharge from steep uphill areas. The zonation method was employedmore » to account for the clustering of high and low hydraulic conductivities measured in a geologic unit. A composite model was used to represent the bulk effect of thin layers of relatively high hydraulic conductivity found within bedrock of otherwise low conductivity. The inverse simulator ITOUGH2 was used to calibrate the model for the distribution of rock properties. The model was initially calibrated using data collected between 1994 and 1996. To check the validity of the model, it was subsequently applied to predicting groundwater level fluctuation and groundwater flux between 1996 and 1998. Comparison of simulated and measured data demonstrated that the model is capable of predicting the complex flow reasonably well. Advective transport was approximated using pathways of particles originating from source areas of the plumes. The advective transport approximation was in good agreement with the trend of contaminant plumes observed over the years. The validated model was then refined to focus on a subsection of the large system. The refined model was subsequently used to assess the efficiency of hydraulic measures implemented for remediation.« less
  • A linked set of Monte Carlo applications has been developed in order to investigate the sputtering, deposition, and ionization processes in a circular direct current unbalanced magnetron discharge. Particles respond to prescribed electric and magnetic fields, the former taken from experimental measurements, and self-consistent plasma behavior resulting in changes in the fields is not accounted for. The motion of energetic electrons emitted from the target surface by ion impacts is followed in the gas phase in order to characterize ionization and excitation collisions and elastic scattering with argon filling gas. The inhomogeneous erosion track profile is computed and compared withmore » experimental measurements. The transport of titanium sputtered neutrals between the target and substrate surfaces is then analyzed using both a rigid sphere collision model and an interatomic potential model to describe collisions between sputtered neutrals and background gas atoms. The radial emission distribution of sputtered atoms is taken from the electron transport model. The mean arrival energy and the angular distribution of titanium neutrals impinging on the substrate surface, and the metal density profile between target and substrate are calculated. Finally, the electron impact ionization of titanium neutrals in a plasma formed by a mixture of titanium (10% of argon density) and argon atoms is simulated, motivated by the promising possibility of controlling the deposition process by influencing the direction of the ion flux.« less