Global Reliability Sensitivity Analysis Based on Maximum Entropy and 2-Layer Polynomial Chaos Expansion
To optimize contributions of uncertain input variables on the statistical parameter of given model, e.g., reliability, global reliability sensitivity analysis (GRSA) provides an appropriate tool to quantify the effects. However, it may be difficult to calculate global reliability sensitivity indices...
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doaj-e0b0445cea324de284796c50bb01ed502020-11-24T23:42:31ZengMDPI AGEntropy1099-43002018-03-0120320210.3390/e20030202e20030202Global Reliability Sensitivity Analysis Based on Maximum Entropy and 2-Layer Polynomial Chaos ExpansionJianyu Zhao0Shengkui Zeng1Jianbin Guo2Shaohua Du3School of Reliability and Systems Engineering, Beihang University, Beijing 100191, ChinaSchool of Reliability and Systems Engineering, Beihang University, Beijing 100191, ChinaSchool of Reliability and Systems Engineering, Beihang University, Beijing 100191, ChinaCRRC ZIC Research Institute of Electrical Technology & Material Engineering, Zhuzhou 412001, ChinaTo optimize contributions of uncertain input variables on the statistical parameter of given model, e.g., reliability, global reliability sensitivity analysis (GRSA) provides an appropriate tool to quantify the effects. However, it may be difficult to calculate global reliability sensitivity indices compared with the traditional global sensitivity indices of model output, because statistical parameters are more difficult to obtain, Monte Carlo simulation (MCS)-related methods seem to be the only ways for GRSA but they are usually computationally demanding. This paper presents a new non-MCS calculation to evaluate global reliability sensitivity indices. This method proposes: (i) a 2-layer polynomial chaos expansion (PCE) framework to solve the global reliability sensitivity indices; and (ii) an efficient method to build a surrogate model of the statistical parameter using the maximum entropy (ME) method with the moments provided by PCE. This method has a dramatically reduced computational cost compared with traditional approaches. Two examples are introduced to demonstrate the efficiency and accuracy of the proposed method. It also suggests that the important ranking of model output and associated failure probability may be different, which could help improve the understanding of the given model in further optimization design.http://www.mdpi.com/1099-4300/20/3/202global reliability sensitivity analysispolynomial chaos expansionSobol’s indicesthe maximum entropy method |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Jianyu Zhao Shengkui Zeng Jianbin Guo Shaohua Du |
spellingShingle |
Jianyu Zhao Shengkui Zeng Jianbin Guo Shaohua Du Global Reliability Sensitivity Analysis Based on Maximum Entropy and 2-Layer Polynomial Chaos Expansion Entropy global reliability sensitivity analysis polynomial chaos expansion Sobol’s indices the maximum entropy method |
author_facet |
Jianyu Zhao Shengkui Zeng Jianbin Guo Shaohua Du |
author_sort |
Jianyu Zhao |
title |
Global Reliability Sensitivity Analysis Based on Maximum Entropy and 2-Layer Polynomial Chaos Expansion |
title_short |
Global Reliability Sensitivity Analysis Based on Maximum Entropy and 2-Layer Polynomial Chaos Expansion |
title_full |
Global Reliability Sensitivity Analysis Based on Maximum Entropy and 2-Layer Polynomial Chaos Expansion |
title_fullStr |
Global Reliability Sensitivity Analysis Based on Maximum Entropy and 2-Layer Polynomial Chaos Expansion |
title_full_unstemmed |
Global Reliability Sensitivity Analysis Based on Maximum Entropy and 2-Layer Polynomial Chaos Expansion |
title_sort |
global reliability sensitivity analysis based on maximum entropy and 2-layer polynomial chaos expansion |
publisher |
MDPI AG |
series |
Entropy |
issn |
1099-4300 |
publishDate |
2018-03-01 |
description |
To optimize contributions of uncertain input variables on the statistical parameter of given model, e.g., reliability, global reliability sensitivity analysis (GRSA) provides an appropriate tool to quantify the effects. However, it may be difficult to calculate global reliability sensitivity indices compared with the traditional global sensitivity indices of model output, because statistical parameters are more difficult to obtain, Monte Carlo simulation (MCS)-related methods seem to be the only ways for GRSA but they are usually computationally demanding. This paper presents a new non-MCS calculation to evaluate global reliability sensitivity indices. This method proposes: (i) a 2-layer polynomial chaos expansion (PCE) framework to solve the global reliability sensitivity indices; and (ii) an efficient method to build a surrogate model of the statistical parameter using the maximum entropy (ME) method with the moments provided by PCE. This method has a dramatically reduced computational cost compared with traditional approaches. Two examples are introduced to demonstrate the efficiency and accuracy of the proposed method. It also suggests that the important ranking of model output and associated failure probability may be different, which could help improve the understanding of the given model in further optimization design. |
topic |
global reliability sensitivity analysis polynomial chaos expansion Sobol’s indices the maximum entropy method |
url |
http://www.mdpi.com/1099-4300/20/3/202 |
work_keys_str_mv |
AT jianyuzhao globalreliabilitysensitivityanalysisbasedonmaximumentropyand2layerpolynomialchaosexpansion AT shengkuizeng globalreliabilitysensitivityanalysisbasedonmaximumentropyand2layerpolynomialchaosexpansion AT jianbinguo globalreliabilitysensitivityanalysisbasedonmaximumentropyand2layerpolynomialchaosexpansion AT shaohuadu globalreliabilitysensitivityanalysisbasedonmaximumentropyand2layerpolynomialchaosexpansion |
_version_ |
1725504180190183424 |