Abstract
Although controller devices highly improve the seismic performance of civil structures, they usually incur enormous financial costs. A variety of sequential methods for minimizing the cost function have been proposed in the literature. In most of these methods, the control system is optimally designed after the best structural configuration is provided. However, such sequential procedures are unable to yield the best overall design. This paper discusses a combined structural and control optimization approach in which the structural mass and controlled system energy are simultaneously minimized. To this end, a twofold objective function is defined by linearly combining the structural mass and linear quadratic regulator (LQR) performance index. It is shown that the optimal value of this objective function depends on the initial condition, and to circumvent this problem, an alternative objective function is introduced which allows for solving the problem of initial condition dependency. Given the complexity of the problem, a variable neighborhood search (VNS) metaheuristic method is developed. The performance of the developed method is demonstrated through case studies involving the determination of structural responses for shear-type frames. The case studies are presented for evaluating and comparing the effectiveness of the proposed simultaneous technique and the conventional sequential method. The responses of the structures are determined under an array of strong ground motions. The results of the comparative analyses revealed that the simultaneously optimized cases using the proposed methodology had superior dynamic performance compared to the sequentially optimized cases.
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Acknowledgments
This paper and the research behind it are sincerely devoted to Prof. Mohamad Ali Hajabasi, Faculty member of the Mechanical Engineering Department at Shahid Bahonar University of Kerman, Iran for his unstinting help and constructive suggestions while the idea was in gestation. His willingness to give his time so generously has been very much appreciated.
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Implementation of the proposed method was undertaken using the MATLAB R2015b (MATLAB R2015b 2015) platform. All developed codes and models supporting the findings of this study are available from the authors upon reasonable request.
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Alavi, A., Dolatabadi, M., Mashhadi, J. et al. Simultaneous optimization approach for combined control–structural design versus the conventional sequential optimization method. Struct Multidisc Optim 63, 1367–1383 (2021). https://doi.org/10.1007/s00158-020-02765-3
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DOI: https://doi.org/10.1007/s00158-020-02765-3