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A constrained Bayesian Optimization framework for structural vibrations with local nonlinearities
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DOI：10.1007/s00158-024-03747-5.png)
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In order to address stringent standards, energy efficiency objectives or also cost reduction imperatives, the optimal design of complex industrial structures is an important concern. In this context, parametric optimization offers a powerful tool for engineers. Taking into account nonlinear behavior in the models allows performing high-fidelity numerical simulations and thus reducing safety margins. However, in vibration dynamics, the use of classical global optimization methods on industrial-scale structures with nonlinearities is not affordable due to too many required solver calls to localize the optimum. This work proposes an approach to achieve global constrained optimization of structures with local nonlinearities in vibration. The strategy is based on a Bayesian Optimization process relying on two tools: (i) a Gaussian Process as a surrogate model and (ii) a dedicated nonlinear mechanical solver based on the Harmonic Balance Method. These two tools are presented in detail. Their performance and characteristics are presented and analyzed on academic and industrial-scale examples. The whole strategy is finally applied on a Duffing oscillator without optimization's constraint and a gantry crane to illustrate the efficiency on constrained optimization. In addition, many discussions are made relative to the number of initial sample points. The results show that the proposed approach is able to find the global optimum with a limited number of solver calls, demonstrating its ability to be integrated into an actual industrial design process.
Keyword:
Constrained global optimization
Nonlinear vibration
Bayesian Optimization
Gaussian Process
Harmonic Balance Method
Duffing oscillator
Gantry crane
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