Advanced Dimension-Adaptive Sparse Grid Integration Method for Structural Reliability Analysis
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7, Issue 3
Abstract
The conventional sparse grid (SG) integration method treats all considered random variables equally for the numerical integration of performance functions. The dimension-equal treatment inevitably causes a considerable demand of computation devoted to unimportant variables. To overcome this shortcoming, an advanced dimension-adaptive sparse grid (ADASG) integration method is proposed by introducing a numerical indicator quantifying the importance levels of tensor products of difference quadrature formulas. By achieving a target number of function evaluations, only several important tensor products of difference quadrature formulas are retained while the unimportant ones are removed. The proposed ADASG integration method is firstly employed to estimate the first four moments of performance functions. The estimated moments are then applied to structural reliability analysis by generating the probability density function of performance functions using the maximum entropy method. The advantage of the proposed ADASG integration method is demonstrated over four examples. The reliability index calculated by the proposed ADASG integration method shows favorable consistency to that obtained by the direct Monte Carlo simulation. Compared with conventional SG integration methods, the proposed ADASG integration method exhibits a better performance in terms of both accuracy and efficiency.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. Available items include the matrix data files and program codes for numerical examples.
Acknowledgments
The financial support received from the National Science Foundation of China (Grant Nos. 51778198 and 51808397) is gratefully appreciated.
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ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7 • Issue 3 • September 2021
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© 2021 American Society of Civil Engineers.
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Received: Nov 9, 2020
Accepted: Mar 16, 2021
Published online: Jun 4, 2021
Published in print: Sep 1, 2021
Discussion open until: Nov 4, 2021
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