This paper proposes an active learning-based Gaussian process (AL-GP) metamodelling method to estimate the cumulative as well as complementary cumulative distribution function (CDF/CCDF) for forward uncertainty quantification (UQ) problems. Within the field of UQ, previous studies focused on developing AL-GP approaches for reliability (rare event probability) analysis of expensive black-box solvers. A naive iteration of these algorithms with respect to different CDF/CCDF threshold values would yield a discretized CDF/CCDF. However, this approach inevitably leads to a trade off between accuracy and computational efficiency since both depend (in opposite way) on the selected discretization. In this study, a specialized error measure and a learning function are developed such that the resulting AL-GP method is able to efficiently estimate the CDF/CCDF for a specified range of interest without an explicit dependency on discretization. Particularly, the proposed AL-GP method is able to simultaneously provide accurate CDF and CCDF estimation in their median-low probability regions. Three numerical examples are introduced to test and verify the proposed method.

A novel active learning-based Gaussian process metamodelling strategy for estimating the full probability distribution in forward UQ analysis / Wang, Ziqi; Broccardo, Marco. - In: STRUCTURAL SAFETY. - ISSN 0167-4730. - 84:(2020), pp. 101937.1-101937.16. [10.1016/j.strusafe.2020.101937]

A novel active learning-based Gaussian process metamodelling strategy for estimating the full probability distribution in forward UQ analysis

Broccardo, Marco
2020-01-01

Abstract

This paper proposes an active learning-based Gaussian process (AL-GP) metamodelling method to estimate the cumulative as well as complementary cumulative distribution function (CDF/CCDF) for forward uncertainty quantification (UQ) problems. Within the field of UQ, previous studies focused on developing AL-GP approaches for reliability (rare event probability) analysis of expensive black-box solvers. A naive iteration of these algorithms with respect to different CDF/CCDF threshold values would yield a discretized CDF/CCDF. However, this approach inevitably leads to a trade off between accuracy and computational efficiency since both depend (in opposite way) on the selected discretization. In this study, a specialized error measure and a learning function are developed such that the resulting AL-GP method is able to efficiently estimate the CDF/CCDF for a specified range of interest without an explicit dependency on discretization. Particularly, the proposed AL-GP method is able to simultaneously provide accurate CDF and CCDF estimation in their median-low probability regions. Three numerical examples are introduced to test and verify the proposed method.
2020
Wang, Ziqi; Broccardo, Marco
A novel active learning-based Gaussian process metamodelling strategy for estimating the full probability distribution in forward UQ analysis / Wang, Ziqi; Broccardo, Marco. - In: STRUCTURAL SAFETY. - ISSN 0167-4730. - 84:(2020), pp. 101937.1-101937.16. [10.1016/j.strusafe.2020.101937]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/286214
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