A Novel BACG Inverse Reliability Algorithm for Efficient and Robust Reliability-Based Topology Optimization of Marine Structures

Reliability assessment (RA) is pivotal to enhancing the efficiency and robustness of reliability-based optimization. Classical RA algorithms suffer from inefficiency and non-convergence problems such as bifurcation, periodic oscillations, and chaos. In this paper, a bi-directional adaptive conjugate gradient (BACG) algorithm incorporating a newly developed concave vs. convex decision criterion (CCDC) is suggested. The BACG technique is harmoniously fused with the sequential optimization and reliability assessment (SORA) to expedite design timelines while simultaneously enhancing precision. Within the BACG, an adaptive acceleration factor is presented to dynamically activate the positive and negative acceleration of the most probable point (MPP) search, specifically tailored for convex and concave performance functions. The concavity/convexity of the performance function is adjudicated via the CCDC using two adjoining MPPs. The validation of the convergence of BACG is established through rigorous mathematical formulation. A comprehensive study is conducted to assess the robustness, stability, and efficiency of BACG via matching with eight prominent inverse RA methods. The study encompasses six inverse reliability problems, one reliability-based design optimization (RBDO), and two reliability-based topology optimization (RBTO) projects involving a simply supported beam and a submarine pressure hull. Lastly, the BACG is utilized to perform the RBTO design for a jacket offshore platform.