دورية أكاديمية
Scarce Sample-Based Reliability Estimation and Optimization Using Importance Sampling
| العنوان: | Scarce Sample-Based Reliability Estimation and Optimization Using Importance Sampling |
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| المؤلفون: | Kiran Pannerselvam, Deepanshu Yadav, Palaniappan Ramu |
| المصدر: | Mathematical and Computational Applications, Vol 27, Iss 6, p 99 (2022) |
| بيانات النشر: | MDPI AG, 2022. |
| سنة النشر: | 2022 |
| المجموعة: | LCC:Applied mathematics. Quantitative methods LCC:Mathematics LCC:Electronic computers. Computer science |
| مصطلحات موضوعية: | reliability, importance sampling, scarce data, surrogate, RBDO, MOO, Applied mathematics. Quantitative methods, T57-57.97, Mathematics, QA1-939, Electronic computers. Computer science, QA75.5-76.95 |
| الوصف: | Importance sampling is a variance reduction technique that is used to improve the efficiency of Monte Carlo estimation. Importance sampling uses the trick of sampling from a distribution, which is located around the zone of interest of the primary distribution thereby reducing the number of realizations required for an estimate. In the context of reliability-based structural design, the limit state is usually separable and is of the form Capacity (C)–Response (R). The zone of interest for importance sampling is observed to be the region where these distributions overlap each other. However, often the distribution information of C and R themselves are not known, and one has only scarce realizations of them. In this work, we propose approximating the probability density function and the cumulative distribution function using kernel functions and employ these approximations to find the parameters of the importance sampling density (ISD) to eventually estimate the reliability. In the proposed approach, in addition to ISD parameters, the approximations also played a critical role in affecting the accuracy of the probability estimates. We assume an ISD which follows a normal distribution whose mean is defined by the most probable point (MPP) of failure, and the standard deviation is empirically chosen such that most of the importance sample realizations lie within the means of R and C. Since the probability estimate depends on the approximation, which in turn depends on the underlying samples, we use bootstrap to quantify the variation associated with the low failure probability estimate. The method is investigated with different tailed distributions of R and C. Based on the observations, a modified Hill estimator is utilized to address scenarios with heavy-tailed distributions where the distribution approximations perform poorly. The proposed approach is tested on benchmark reliability examples and along with surrogate modeling techniques is implemented on four reliability-based design optimization examples of which one is a multi-objective optimization problem. |
| نوع الوثيقة: | article |
| وصف الملف: | electronic resource |
| اللغة: | English |
| تدمد: | 2297-8747 1300-686X |
| العلاقة: | https://www.mdpi.com/2297-8747/27/6/99Test; https://doaj.org/toc/1300-686XTest; https://doaj.org/toc/2297-8747Test |
| DOI: | 10.3390/mca27060099 |
| الوصول الحر: | https://doaj.org/article/fb0e9374c5e545abb9635049853b4115Test |
| رقم الانضمام: | edsdoj.fb0e9374c5e545abb9635049853b4115 |
| قاعدة البيانات: | Directory of Open Access Journals |
| تدمد: | 22978747 1300686X |
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| DOI: | 10.3390/mca27060099 |