建立了稱為 M-IS（多球體重要性採樣）的 RBIS（基於徑向的重要性採樣）的創新版本。 RBIS 最初是一種基於仿真的可靠性方法，它創建單個球體以排除球體內的採樣域。利用相同的概念，M-IS 產生多個球體而不是單個球體，以進一步排除更多的採樣域。在確定球體位置和半徑時，M-IS 採用自適應框架，確保部署的球體位於安全區域內，並準確地鄰接球體和失效函數面。本研究還介紹了 M-IS 在 RBDO（基於可靠性的設計優化）中的實施。本研究執行雙循環優化，其中元啟發式算法和 M-IS 分別用作外循環和內循環。為了在優化過程中提高效率，採用人工智能（AI）來代替失效函數。在上一次迭代的球體確定過程中，將使用評估樣本饋送內置 AI。在 M-IS 框架中，每個可靠性分析的每個部署球體都需要對部分樣本進行功能評估。有趣的是，這些樣本中的大多數都位於臨界失效表面附近。提議的 RBDO 利用先前 RBDO 迭代期間每個可靠性分析的評估樣本作為 AI 的訓練數據。與其他最近的基於仿真的可靠性方法相比，擬議的 M-IS 顯示出更好的準確性和效率。本論文中演示的 RBDO 程序也顯示出令人滿意的結果，在不犧牲過高的精度的情況下，使用低計算成本解決了幾個結構工程問題。

An innovative version of RBIS (Radial Based Importance Sampling) termed as M-IS (Multisphere Importance Sampling) is established. Originally, RBIS is a simulation based reliability method that create single sphere to exclude sampling domain inside sphere. Utilizing same concept, M-IS produces multiple spheres instead of only single sphere to further exclude more sampling domain. In determining spheres locations and radii, M-IS employ adaptive framework that ensure deployed spheres located inside safety region and accurately adjoining sphere and failure function surfaces. Implementation of M-IS in RBDO (Reliability Based Design Optimization) also presented in this study. This study performs a double-loop optimization in which metaheuristic algorithm and M-IS are used as outer and inner loop respectively. To increase efficiency during optimization, Artificial Intelligence (AI) is adopted to replace failure function. Built AI will be fed using evaluated samples during sphere determination on previous iteration. In M-IS framework, portion of samples are required to be function evaluated for every deployed sphere per reliability analysis. Interestingly, most of those samples are located around the critical failure surface. Proposed RBDO utilizes those evaluated samples from every reliability analysis during previous RBDO iteration to be a training data for AI. Proposed M-IS shows better accuracy and efficiency compared to other recent simulation-based reliability method. Demonstrated RBDO procedure in this dissertation also shows a satisfactory result in solving several structural engineering problems using low computation cost without sacrificing excessive accuracy.

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