LUB: A Novel Adaptive Kriging Framework Incorporating Lower and Upper Bound Analysis for Enhanced Structural Reliability-Based Design Optimization

Abstract

Reliability-based design optimization (RBDO) is increasingly recognized for its potential to enhance the performance of structural engineering systems. Despite its potential, traditional RBDO methods are often hampered by significant computational challenges, especially when applied to nonlinear structures where simultaneous execution of structural optimization and reliability analysis increases the complexity of analysis. This computational burden presents a significant barrier for broader application of RBDO in complex systems, which therefore highlights the need for more efficient approaches. To address this challenge, we introduce an adaptive Kriging-assisted RBDO framework that leverages lower and upper bounds (LUB) analysis to improve its computational efficiency and robustness. In this proposed framework, regions delineated by varying confidence bounds are used for identifying design points close to the limit state. Convergence is rigorously assessed by comparing design and reliability predictions across upper and lower bound interfaces, thereby ensuring both interpretability and robustness. The framework allows for flexibility through its seamless integration with various adaptive sampling processes, evolutionary optimization algorithms, and reliability assessment techniques. The proposed framework is evaluated for four benchmark examples and two engineering cases, demonstrating superior accuracy and efficiency with fewer model evaluations compared with existing approaches. Through iterative optimization, the framework consistently maintains cost and errors of reliability estimation within predefined thresholds, offering robust and computationally efficient solutions.