ESLA: a new surrogate-assisted single-loop reliability-based design optimization technique

Abstract

In this paper, we address the formulation of a novel scheme for reliabilitybased design optimization, in which the design optimization problem is characterized by constraints that must be met with a certain probability. Assessment of the aforementioned is typically referred to as reliability analysis. Conventional methods rely on sampling approaches or by reformulating the problem as a two-level optimization that requires gradient or Hessian information of the constraints to obtain a trustworthy solution. However, the computational cost of such methods makes them often impractical. To overcome the aforementioned, a surrogateassisted asymptotic reliability analysis (SARA) is presented that makes use of surrogate-derived gradient and Hessian information. The sub-optimization problem is reformulated as a set of constraints using the Karush-Kuhn-Tucker conditions and fitted in an efficient global optimization-like setting through the formulation of the reliability-based expected improvement (RBEI), obtaining the novel efficient single-loop approach (ESLA). The method is tested on a series of test cases which prove the effectiveness of the novel scheme.

Design optimization-under-uncertainty of a forward swept wing unmanned aerial vehicle using SAMURAI

“…The optimization of the acquisition function is a computationally cheap problem, since it occurs on the surrogate itself. The methodological cornerstones of SAMURAI: GAMO, 65 ERGO 66 and ESLA 67 formulate novel acquisition functions within the EGO framework to respectively enable asynchronous multi-objective optimization with exploration and exploitation control, RDO by means of an analytical uncertainty propagation through the surrogate and a multi-objective treatment of the problem and RBDO by means of an asymptotic reliability analysis in a single-loop formulation using the KKT-conditions. Combining all the aforementioned, a surrogate-assisted design optimization-under-uncertainty methodology can be created (Figure 2).…”

“…For details, I refer to. 67 Now, the Generalized multi-points Reliability-Based Robust Expected Improvement can be introduced as:…”

“…For details, I refer to. 67 Now, the Generalized multi-points Reliability-Based Robust Expected Improvement can be introduced as: Incorporated in the GAMO-framework 65 the SAMURAI framework is obtained (Algorithm 3). 74…”

Generalized Karagiannidis–Lioumpas Approximations and Bounds to the Gaussian Q-Function With Optimized Coefficients

“…in which the first summation is taken over all combinations of non-negative integer indices p 1 through p N such that the sum of all p n is P . The parameters are G = P p1,p2,...,pN , [16]- [20] from the wide range of applications available in the literature for which the proposed GKL expression is applicable as a substitute for the KL expression that was originally used in those publications. In particular, the GKL approximation/bound can be used to calculate the sampling bit error probability of binary phase shift keying [16], to approximate the phase noise probability density function in the system considered in [17], and to derive the coherent LoRa R symbol error rate under additive white Gaussian noise [18].…”

“…In particular, the GKL approximation/bound can be used to calculate the sampling bit error probability of binary phase shift keying [16], to approximate the phase noise probability density function in the system considered in [17], and to derive the coherent LoRa R symbol error rate under additive white Gaussian noise [18]. Beyond communications, it allows to approximate the distribution functions of particles experiencing compound subdiffusion [19] and to derive the predictive error of the probability of failure [20], for instance.…”