This paper presents a method for the automatic selection of weighting matrices for a linear-quadratic regulator(LQR) in order to design an optimal active structural control system. The weighting matrices of a control performanceindex, which are used to design optimal state-feedback gains, are usually determined by rule of thumbor exhaustive search approaches. To explore an easy way to select optimal parameters, this paper presents amethod based on Bayesian optimization (BO). A 10-degree-of-freedom (DOF) shear building model that haspassive-base isolation (PBI) under the building is used as an example to explain the method. A control performanceindex that contains the absolute acceleration, along with the inter-story drift and velocity of each story, ischosen for the design of the controller. An objective function that contains the maximum absolute acceleration ofthe building is chosen for BO to produce optimal weighting matrices. In the numerical example, a restriction onthe displacement of the PBI is used as a constraint for the selection of weighting matrices. First, the BO method iscompared to the exhaustive search method using two parameters in the weighting matrices to illustrate thevalidity of the BO method. Then, thirty-three parameters (which are automatically optimized by the BO method)in the weighting matrices are used to elaborately tune the controller. The control results are compared to thosefor the exhaustive search method and conventional optimal control, in terms of the control performance of therelative displacement, absolute acceleration, inter-story-drift angle, and the story-shear coefficient of each story.The damping ratio for each mode, and the control energy and power are also compared. The comparison demonstratesthe validity of the method.
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