High-Dimensional Reliability Method Accounting for Important and Unimportant Input Variables

Abstract

Reliability analysis is usually a core element in engineering design and can be performed with physical models (limit-state functions). Reliability analysis becomes computationally expensive when the dimensionality of input random variables is high. This work develops a high dimensional reliability analysis method by a new dimension reduction strategy so that the contributions of unimportant input variables are also accommodated by the dimension reduction. The dimension reduction is performed with the first iteration of the first order reliability method (FORM), which identifies important and unimportant input variables. Then a higher order reliability analysis is performed in the reduced space of only important input variables. The reliability obtained in the reduced space is then integrated with the contributions of unimportant input variables, resulting in the final reliability prediction that accounts for both types of input variables. Consequently, the new reliability method is more accurate than the traditional method, which fixes unimportant input variables at their means. The accuracy is demonstrated by three examples.

Probabilistic Assessment of Structural Integrity

“…It consistently produces a reliably structured outcome, requiring no specialized analysts or extraordinary efforts beyond the prevailing deterministic methods. The FORM ensures the effective integration of design uncertainty and facilitates the verification of reliability responses [10,17].…”

Unsupervised and supervised learning for the reliability analysis of complex systems

“…The high‐dimensional reliability is estimated by capturing the limit state function in the latent space using Gaussian process regression. Focused on structural reliability in Yi and Du, 4 it is presented a new dimension reduction strategy based on the first‐order reliability method (FORM) so that the contributions of unimportant input variables are also accommodated after dimension reduction.…”

Active learning with generalized sliced inverse regression for high-dimensional reliability analysis

“…There are three types of reliability analysis methods: 1) approximation methods [2][3][4], 2) metamodeling methods [5][6][7][8][9][10][11][12], and 3) sampling methods [13][14][15][16][17]. Commonly used approximation methods include the first order reliability method (FORM) [2] and the second order reliability method (SORM) [3].…”