Dimensionality reduction enhances data-driven reliability-based design optimize

Abstract

A recently proposed data-driven approach to reliability-based design optimization of structures constructs a sufficient condition that the target reliability is guaranteed with the specified confidence level, without relying on any assumptions on statistical information of random variables. In general, there exists a gap between this sufficient condition and the original confidence-level constraint. This paper presents a simple dimensionality reduction technique that can possibly mitigate this gap. This technique is applied to the compliance constraint with the uncertain external load. Numerical experiments on truss and continuum examples demonstrate that the proposed method can drastically reduce the over-conservativeness of the original method.

Structural reliability under uncertainty in moments: distributionally-robust reliability-based design optimization

“…4.1, we consider, not only the normal distributions, but all of the probability distributions with and belonging to the uncertainty set. That is, the set of possible realizations of probability distributions is given by (35). Figure 8 displays the variations in the optimal value with respect to the failure probability, , and the uncertainty magnitudes and (in the same manner as above, the values of ∈ [0, 0.02] are varied in a manner proportional to ).…”

“…As in Sect. 4.1, we require the reliability constraint to be satisfied for all the probability distributions satisfying ∈ U and ∈ U , i.e., for any probability distribution belonging to P in (35). For the 2 -norm uncertainty, Fig.…”

“…Zhang et al [64] proposed the use of the distributional probability box (the distributional p-box) [52] for RBDO with limited data of uncertain variables. 4 Kanno [34,35] and Jekel and Haftka [27] proposed RBDO methods using order statistics. The methods in [27,34,35], which were based on the order statistics, did not make any assumptions regarding the statistical information of the uncertain parameters, and used random samples of the uncertain parameters directly to guarantee the confidence of the target reliability.…”

Computation‐with‐confidence for static elasticity: Data‐driven approach with order statistics

“…Instead, we require that the probability that the reliability constraint formulated above is satisfied is no smaller than the target confidence level. This requirement is motivated by the constraint considered in RBDO with an uncertain input probability distribution [34][35][36][37][38][39][40][41]. In a manner similar to Kanno [38], we derive a sufficient condition for this confidence level requirement by using the order statistics of the given data points.…”

Structural reliability under uncertainty in moments: distributionally-robust reliability-based design optimization

“…Zhang et al [53] proposed to use the distributional probability box (the distributional p-box) [41] for RBDO with limited data of uncertain variables. Kanno [29,30] and Jekel and Haftka [23] proposed RBDO methods using order statistics. These methods, based on the order statistics, do not make any assumption on statistical information of uncertain parameters, and use random samples of uncertain parameters directly to guarantee confidence of the target reliability.…”