A heuristic moment-based framework for optimization design under uncertainty
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ORIGINAL ARTICLE
A heuristic moment‑based framework for optimization design under uncertainty Kuo‑Wei Liao1 · Nophi Ian D. Biton2 Received: 4 December 2018 / Accepted: 22 April 2019 © Springer-Verlag London Ltd., part of Springer Nature 2019
Abstract To search an optimal design under uncertainty, this study proposes an effective framework that integrates the moment-based reliability analysis into a heuristic optimization algorithm. Integration of an equivalent single-variable performance function is an ideal concept to calculate the failure probability. However, such integration is often not available and is alternatively computed using the first four moments and a generalized moment-based reliability index is established, in which the Gaussian–Hermite integration and dimension reduction are implemented to enhance the effectiveness. To overcome the limited applicable range of moment-based approach, an adjustable optimization procedure is proposed, in which different reliability methods are performed depending on results of the constraint assessments. In addition, the ε level comparison is integrated into particle-swarm optimization to consider the constraint violation. Several literature studies are used to verify the accuracy of the proposed optimization framework including problems having linear, highly nonlinear, implicit probabilistic constraint functions with normal or non-normal variables and system-level reliability analysis. The effects of several parameters, such as the number of estimate point, the number of dimension, and the degree of uncertainty, are thoroughly investigated. Results indicating that tri-variate with seven points are able to provide a stable solution under a high degree of uncertainty. Keywords Risk and reliability · Safety · Uncertainty · Probabilistic design · Optimization techniques
1 Introduction Uncertainties in an engineering design problem are often inevitable; to ensure a greater performance, reliability-based design optimization (RBDO) is often adopted. A traditional RBDO is a nested double-loop approach in which the outer loop is the deterministic optimization, and the inner loop is the reliability analysis, which is often a barrier in application. To simplify the computational complexity of an RBDO problem, many algorithms have been proposed. For example, safety factor has been adopted in many design codes to take uncertainties into consideration. The safety factor approach, however, often fails to identify the relative
* Kuo‑Wei Liao [email protected] Nophi Ian D. Biton [email protected] 1
Department of Bioenvironmental Systems Engineering, National Taiwan University, Taipei, Taiwan
University of San Carlos-Cebu, Cebu City, Philippines
2
importance among design parameters, because all uncertainties are represented by s single factor throughout the design [11]. Du and Chen [2] proposed the sequential optimization and reliability assessment (SORA) to sequentially conduct the deterministic optimization and inverse reliability analysis until the solution converge
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