POFDarts: Geometric adaptive sampling for probability of failure
Abstract
We introduce a novel technique, POFDarts, to estimate the Probability Of Failure based on random diskpacking in the uncertain parameter space. POFDarts 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 nonfailure 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:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States); Univ. of Texas, Austin, TX (United States)
 Publication Date:
 Research Org.:
 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1262234
 Report Number(s):
 SAND20166079J
Journal ID: ISSN 09518320; PII: S095183201630045X
 Grant/Contract Number:
 AC0494AL85000
 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 09518320
 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. POFDarts: 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. POFDarts: 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.
"POFDarts: 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 = {POFDarts: 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, POFDarts, to estimate the Probability Of Failure based on random diskpacking in the uncertain parameter space. POFDarts 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 nonfailure 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
}
Web of Science


Efficient evaluation of small failure probability in highdimensional groundwater contaminant transport modeling via a twostage Monte Carlo method: FAILURE PROBABILITY
In decisionmaking 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 CPUdemanding 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 highdimensional models, i.e., models containing many uncertain input parameters.more » 
Fourdimensional cone beam CT with adaptive gantry rotation and adaptive data sampling
We have developed a new fourdimensional cone beam CT (4DCBCT) on a Varian imageguided 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 realtime positioning and monitoring system to record the respiratory signal of the patient during the acquisition of the CBCT data. We used the fullfanmore » 
Efficiently sampling conformations and pathways using the concurrent adaptive sampling (CAS) algorithm
Molecular dynamics (MD) simulations are useful in obtaining thermodynamic and kinetic properties of biomolecules 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 highdimensional 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 »