SYSTEM-RELIABILITY-BASED DESIGN OPTIMIZATION OF TRUSS STRUCTURES CONSIDERING FATIGUE-INDUCED SEQUENTIAL FAILURE

Abstract

Civil infrastructure, such as bridges, power transmission towers and offshore structures, are constantly subjected to cyclic environmental and/or live loads over their life spans. Fatigue stresses develop owing to repeated loading, which can induce an overall collapse of the structure. Due to the costly and catastrophic consequences of the system failure, structural design procedures should consider fatigue- induced failures. Truss structures are commonly used owing to their efficiency in carrying external loads. The redundancy inherent in statically indeterminate trusses allows stress redistribution, which can lead to a series of member failures before a system-level failure is observed. Therefore, fatigue-induced sequential failures must be considered during the structural design stage. Moreover, the fatigue process is a highly random phenomenon; thus, probability-based design is desirable that captures different types of uncertainties (that is, epistemic and aleatory). In addition, engineering design optimization frameworks have been increasingly developed to systematically select the best design that satisfies engineering constraints related to performance and/or safety. System reliability-based design optimization (SRBDO) is a probabilistic optimization framework that explicitly accounts for the uncertainty in system-level performance. Structural optimization, which explicitly considers different sources of uncertainty and accounts for sequential failures, poses several challenges. Firstly, owing to stress redistribution, searching for failure sequences is computationally expensive. This is further aggravated when uncertainty is included, which requires structural system reliability (SSR) analysis. Secondly, some optimization algorithms require gradients with respect to the design variables. Because the critical failure sequence changes when the design of a structure changes, it is difficult to calculate the sensitivity. Finally, incomplete statistical information (that is, epistemic uncertainty) on random parameters makes the reliability of the structure subjective or uncertain. Epistemic uncertainty requires careful consideration when assessing the failure probability of a structure, which leads to further computational costs. This study fills a research gap regarding the application of SRBDO against fatigue-induced sequential failures. Several enhancements and new frameworks are proposed for implementing SRBDO against sequential fatigue-induced failures. First, a gradient-based optimization formulation of SRBDO was developed by proposing a modified sequential compounding (mSCM) method, which is an SSR analysis method that calculates the reliability of a system through successive compounding of its component events. The mSCM is integrated into an improved version of the branch-and-bound algorithm (called B3 method) to search for failure sequences and calculate the overall system failure probability. Furthermore, the Chun-Song-Paulino gradient calculation strategy was utilized to solve the sensitivity with respect to the design parameters. Second, a gradient-free optimizer, specifically, grey wolf optimization (GWO), was used to perform SRBDO. An additional stopping criterion is suggested to further reduce the computational cost of population-based GWO without compromising the optimal design search. Finally, owing to the different types of uncertainty that can arise in practical situations, accounting for epistemic uncertainty (due to an insufficient of knowledge) in the SRBDO framework was developed. A Bayesian approach was used to infer the statistical distribution of the lower and upper reliability bounds produced using the B3 method. A new confidence measure was proposed to assess the design of the structure given the presence of epistemic uncertainty. All developed frameworks were demonstrated using numerical and truss examples. The proposed methods were shown to be effective in determining the optimal designs. Further discussions on the effectiveness and limitations of the proposed framework are included.