# 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:

- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- 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

- Alternate Identifier(s):
- OSTI ID: 1440389

- Report Number(s):
- SAND-2016-6079J

Journal ID: ISSN 0951-8320; PII: S095183201630045X

- Grant/Contract Number:
- AC04-94AL85000; 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. Sat .
"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 = {Sat Jun 18 00:00:00 EDT 2016},

month = {Sat Jun 18 00:00:00 EDT 2016}

}

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