Multiobjective Reliability-Based Design Optimization of the Fuzzy Logic Controller for MR Damper-Based Structures

To devise an optimum and robust fuzzy logic controller for MR damper-based structures subjected to earthquake ground motions, the multiobjective reliability-based design optimization (RBDO) using the adaptive Kriging model is performed to determine the parameters of the fuzzy logic controller. The optimization problem is formulated with two objective functions, namely, the minimization of interstory drift and average control force of the concerned structure, and subjected to a probability constraint on structural dynamic responses under the effects of random structural stiffness and stochastic earthquake loadings. To reduce the computational cost of reliability assessment, a global Kriging model is constructed in an augmented space as a surrogate for computational evaluations. Subsequently, the trained metamodel combined with the nondominated sorting genetic algorithm (NSGA-II) is integrated into the framework of RBDO for solving the fuzzy logic control (FLC) optimization problem. The feasibility and effectiveness of the multiobjective RBDO in the FLC design are finally validated by conducting numerical simulations on both linear and nonlinear structures. As demonstrated in the linear case, the fuzzy logic controllers obtained from the multiobjective RBDO show more robustness than those derived from the multiobjective deterministic design optimization (DDO). In the nonlinear case, using the multiobjective DDO to prelocate a coarse safety domain can significantly reduce the number of samples for training the metamodel and facilitate the implementation of the multiobjective RBDO; in addition, the controlled structural performance with a specified fuzzy logic controller can be further improved by considering MR damper distribution optimization.