Life‐cycle reliability‐based robust design optimization for GP model with response uncertainty

Abstract

Reliability-based robust design optimization (RBRDO) is a crucial tool for lifecycle quality improvement. Gaussian process (GP) model is an effective alternative modeling technique that is widely used in robust parameter design. However, there are few studies to deal with reliability-based design problems by using GP model. This article proposes a novel life-cycle RBRDO approach concerning response uncertainty under the framework of GP modeling technique. First, the hyperparameters of GP model are estimated by using the Gibbs sampling procedure. Second, the expected partial derivative expression is derived based on GP modeling technique. Moreover, a novel failure risk cost function is constructed to assess the life-cycle reliability. Then, the quality loss function and confidence interval are constructed by simulated outputs to evaluate the robustness of optimal settings and response uncertainty, respectively. Finally, an optimization model integrating failure risk cost function, quality loss function, and confidence interval analysis approach is constructed to find reasonable optimal input settings. Two case studies are given to illustrate the performance of the proposed approach. The results show that the proposed approach can make better trade-offs between the quality characteristics and reliability requirements by considering response uncertainty.

An active learning Bayesian ensemble surrogate model for structural reliability analysis

“…And the last one is a ten‐bar truss problem with an implicit performance function. For comparison, four reliability analysis methods based on the single surrogate model are used: (a) the AK‐MCS+U method, 33 (b) the active‐learning reliability combined with the bootstrap polynomial chaos expansion (ALR‐bPCE), 16 (c)the active learning reliability based on the SVR model (ALR‐SVR), 40 and (d) the active learning reliability based on the ensemble learning of surrogate models (ALR‐ELSM) 29 . These four methods are implemented using the UQLab toolbox 41 .…”

“…In the existing surrogate‐based reliability analysis combined with adaptive sampling design, several surrogate models, such as Kriging, 10,11 polynomial chaos expansion (PCE), 12,13 and support vector regression (SVR), 14,15 are frequently used. Kriging is the most popular surrogate model due to its attractive characteristic which can provide both the predicted mean value and variance of unsampled points 16–18 . PCE can represent a random process in terms of orthogonal basis functions, which is considered to be an efficient surrogate modeling technique because of the global convergence properties 19 .…”

“…Kriging is the most popular surrogate model due to its attractive characteristic which can provide both the predicted mean value and variance of unsampled points. [16][17][18] PCE can represent a random process in terms of orthogonal basis functions, which is considered to be an efficient surrogate modeling technique because of the global convergence properties. 19 However, the above two methods are based on the minimization of the empirical risk, and their performance depends largely on the size of the training sample set.…”

Efficient global optimization with co‐evolutionary strategy for asymmetric minimax problem in robust design

“…Robust optimization (RO) seeks optimal decision for some performance metrics, considering uncontrolled sources of variation. 1,2 To improve the quality and reliability of the system being designed, RO can be used to adjust the design parameters of the system to the best possible values and at the same time make the system resilient to risks arising from uncertainty factors. The design parameters of these RO problems are often defined as control factors 𝒙 c , and these uncertainty factors are defined as noise factors 𝒙 n .…”

“…Based on this approach, a number of evolutionary algorithms (EAs) [16][17][18] have been proposed to solve the problem (1). But most of them are only for solving the case where the problem (1) satisfies condition (2), because they adopt a similar and symmetric approach to update xc and xn . With the asymmetric coevolutionary strategy, some EAs 10,18 can solve the problem (1) that does not satisfy condition (2).…”