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

Title: POF-Darts: Geometric adaptive sampling for probability of failure

Abstract

We introduce a novel technique, POF-Darts, to estimate the Probability Of Failure based on random disk-packing in the uncertain parameter space. POF-Darts uses hyperplane sampling to explore the unexplored part of the uncertain space. We use the function evaluation at a sample point to determine whether it belongs to failure or non-failure regions, and surround it with a protection sphere region to avoid clustering. We decompose the domain into Voronoi cells around the function evaluations as seeds and choose the radius of the protection sphere depending on the local Lipschitz continuity. As sampling proceeds, regions uncovered with spheres will shrink, improving the estimation accuracy. After exhausting the function evaluation budget, we build a surrogate model using the function evaluations associated with the sample points and estimate the probability of failure by exhaustive sampling of that surrogate. In comparison to other similar methods, our algorithm has the advantages of decoupling the sampling step from the surrogate construction one, the ability to reach target POF values with fewer samples, and the capability of estimating the number and locations of disconnected failure regions, not just the POF value. Furthermore, we present various examples to demonstrate the efficiency of our novel approach.

Authors:
 [1];  [1];  [1];  [1];  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Univ. of Texas, Austin, TX (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1262234
Report Number(s):
SAND-2016-6079J
Journal ID: ISSN 0951-8320; PII: S095183201630045X
Grant/Contract Number:
AC04-94AL85000
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Reliability Engineering and System Safety
Additional Journal Information:
Journal Volume: 155; Journal Issue: C; Journal ID: ISSN 0951-8320
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; probability of failure; percentile estimation; reliability; computational geometry; surrogate models

Citation Formats

Ebeida, Mohamed S., Mitchell, Scott A., Swiler, Laura P., Romero, Vicente J., and Rushdi, Ahmad A. POF-Darts: Geometric adaptive sampling for probability of failure. United States: N. p., 2016. Web. doi:10.1016/j.ress.2016.05.001.
Ebeida, Mohamed S., Mitchell, Scott A., Swiler, Laura P., Romero, Vicente J., & Rushdi, Ahmad A. POF-Darts: Geometric adaptive sampling for probability of failure. United States. doi:10.1016/j.ress.2016.05.001.
Ebeida, Mohamed S., Mitchell, Scott A., Swiler, Laura P., Romero, Vicente J., and Rushdi, Ahmad A. 2016. "POF-Darts: Geometric adaptive sampling for probability of failure". United States. doi:10.1016/j.ress.2016.05.001. https://www.osti.gov/servlets/purl/1262234.
@article{osti_1262234,
title = {POF-Darts: Geometric adaptive sampling for probability of failure},
author = {Ebeida, Mohamed S. and Mitchell, Scott A. and Swiler, Laura P. and Romero, Vicente J. and Rushdi, Ahmad A.},
abstractNote = {We introduce a novel technique, POF-Darts, to estimate the Probability Of Failure based on random disk-packing in the uncertain parameter space. POF-Darts uses hyperplane sampling to explore the unexplored part of the uncertain space. We use the function evaluation at a sample point to determine whether it belongs to failure or non-failure regions, and surround it with a protection sphere region to avoid clustering. We decompose the domain into Voronoi cells around the function evaluations as seeds and choose the radius of the protection sphere depending on the local Lipschitz continuity. As sampling proceeds, regions uncovered with spheres will shrink, improving the estimation accuracy. After exhausting the function evaluation budget, we build a surrogate model using the function evaluations associated with the sample points and estimate the probability of failure by exhaustive sampling of that surrogate. In comparison to other similar methods, our algorithm has the advantages of decoupling the sampling step from the surrogate construction one, the ability to reach target POF values with fewer samples, and the capability of estimating the number and locations of disconnected failure regions, not just the POF value. Furthermore, we present various examples to demonstrate the efficiency of our novel approach.},
doi = {10.1016/j.ress.2016.05.001},
journal = {Reliability Engineering and System Safety},
number = C,
volume = 155,
place = {United States},
year = 2016,
month = 6
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1work
Citation information provided by
Web of Science

Save / Share:
  • Abstract not provided.
  • 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.more » 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.« less
  • We have developed a new four-dimensional cone beam CT (4D-CBCT) on a Varian image-guided radiation therapy system, which has radiation therapy treatment and cone beam CT imaging capabilities. We adapted the speed of gantry rotation time of the CBCT to the average breath cycle of the patient to maintain the same level of image quality and adjusted the data sampling frequency to keep a similar level of radiation exposure to the patient. Our design utilized the real-time positioning and monitoring system to record the respiratory signal of the patient during the acquisition of the CBCT data. We used the full-fanmore » bowtie filter during data acquisition, acquired the projection data over 200 deg of gantry rotation, and reconstructed the images with a half-scan cone beam reconstruction. The scan time for a 200-deg gantry rotation per patient ranged from 3.3 to 6.6 min for the average breath cycle of 3-6 s. The radiation dose of the 4D-CBCT was about 1-2 times the radiation dose of the 4D-CT on a multislice CT scanner. We evaluated the 4D-CBCT in scanning, data processing and image quality with phantom studies. We demonstrated the clinical applicability of the 4D-CBCT and compared the 4D-CBCT and the 4D-CT scans in four patient studies. The contrast-to-noise ratio of the 4D-CT was 2.8-3.5 times of the contrast-to-noise ratio of the 4D-CBCT in the four patient studies.« less
  • Molecular dynamics (MD) simulations are useful in obtaining thermodynamic and kinetic properties of bio-molecules but are limited by the timescale barrier, i.e., we may be unable to efficiently obtain properties because we need to run microseconds or longer simulations using femtoseconds time steps. While there are several existing methods to overcome this timescale barrier and efficiently sample thermodynamic and/or kinetic properties, problems remain in regard to being able to sample un- known systems, deal with high-dimensional space of collective variables, and focus the computational effort on slow timescales. Hence, a new sampling method, called the “Concurrent Adaptive Sampling (CAS) algorithm,”more » has been developed to tackle these three issues and efficiently obtain conformations and pathways. The method is not constrained to use only one or two collective variables, unlike most reaction coordinate-dependent methods. Instead, it can use a large number of collective vari- ables and uses macrostates (a partition of the collective variable space) to enhance the sampling. The exploration is done by running a large number of short simula- tions, and a clustering technique is used to accelerate the sampling. In this paper, we introduce the new methodology and show results from two-dimensional models and bio-molecules, such as penta-alanine and triazine polymer« less