Sequential simulated annealing for life-cycle optimization of nonlinear stochastic systems via arbitrary polynomial chaos expansion

• Published in: Engineering structures Vol. 304; p. 117675
• Main Authors: dos Santos, Ketson R.M., Beck, André Teófilo, Lopez, Rafael Holdorf
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.04.2024
• Subjects: Performance-based engineering; Polynomial chaos expansion; Simulated annealing; Statistical linearization; Stochastic engineering dynamics; Structural optimization; Performance-based engineering; Structural optimization; Stochastic engineering dynamics; Polynomial chaos expansion; Statistical linearization; Simulated annealing
• ISSN: 0141-0296
• DOI: 10.1016/j.engstruct.2024.117675

Quantifying the uncertainties of engineering systems modeled as nonlinear oscillators subject to random excitation is a theoretically complex and computationally demanding task. Consequently, finding an optimal design of such systems considering their life-cycle performance is prohibitive with Monte Carlo simulation methods. In this paper, an efficient performance-based design optimization approach is developed for finding the optimal parameters of engineering systems modeled as nonlinear/hysteretic oscillators subject to stationary and non-stationary excitation. This novel approach utilizes an arbitrary polynomial chaos expansion to estimate the expected cost of failure without performing a computationally expensive integration over the hazard levels. Moreover, we introduce a novel sequential heuristic optimization scheme based on simulated annealing to minimize the total expected cost over the structure life-cycle. Three examples are included in the paper to assess the developed optimization scheme. First, we use the developed framework to optimize a linear single-degree-of-freedom oscillator subject to broadband excitation. Second, a multi-degree-of-freedom oscillator with cubic nonlinearity in damping and stiffness, subject to stationary broadband excitation, is optimized to show the influence of the problem dimensionality in the optimization process. In the last example, a multi-story reinforced concrete shear building modeled as a multi-degree-of-freedom Bouc-Wen oscillator with stiffness and strength degradation and subject to multi-hazards modeled as stationary (wind excitation) and non-stationary (earthquake) stochastic processes, is optimized. •An efficient performance-based design optimization scheme is developed.•The best design of MDOF systems consider their life-cycle performance.•Statistical linearization is combined with time-variant reliability.•The monetary loss is estimated with an arbitrary polynomial chaos expansion.•A sequential simulated annealing optimization is employed in the framework.