Reliability-Based Topology Optimization for Optimal Layout of Active Controllers of Structures under Random Excitation
Publication: Journal of Engineering Mechanics
Volume 150, Issue 6
Abstract
Topology optimization is an appealing technique for optimal layout of active controllers of structures. However, the existing methods are mainly restricted to deterministic excitations, and the optimal control law involved is determined by use of the classical optimal control (COC) method, in which the sensitivities of the gain matrix with respect to the design variables need to be determined by solving the Riccati sensitivity equation numerically. In this study, a reliability-based topology optimization framework is proposed for optimal layout of active controllers of structures under nonstationary random excitations. The optimization problem is formulated as the minimization of the failure probability of the structure subjected to a specified maximum number of controllers. To avoid solving the Riccati equation, an explicit optimal control (EOC) method is first employed to derive the closed-form optimal control law in terms of the position parameters of controllers. The statistical moments of the optimal control forces and structural responses under random excitations are then obtained explicitly by the operation rules of moments, and the first-passage dynamic reliability of the structure can be formulated using the level-crossing theory. On this basis, the sensitivities of the structural failure probability with respect to the position parameters of controllers can be derived analytically by the direct differential method. Finally, the explicit formulations of the response statistics and the relevant sensitivities are incorporated into a gradient-based method of moving asymptotes (MMA) for topology optimization of the layout of controllers in conjunction with the solid isotropic material with penalization (SIMP) technique. Two numerical examples are presented to demonstrate the feasibility of the proposed topology optimization framework.
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Data Availability Statement
All data, models, and code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The research is funded by the National Natural Science Foundation of China (52178479 and 51678252), the Natural Science Foundation of Guangdong Province (2023A1515012822), and the Guangdong Provincial Key Laboratory of Modern Civil Engineering Technology (2021B1212040003).
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Published In
Journal of Engineering Mechanics
Volume 150 • Issue 6 • June 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Sep 17, 2023
Accepted: Jan 29, 2024
Published online: Apr 9, 2024
Published in print: Jun 1, 2024
Discussion open until: Sep 9, 2024
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