通过强化学习优化梯度超材料的机械能限制和放大
Optimised graded metamaterials for mechanical energy confinement and amplification via reinforcement learning
摘要：
描述了一种设计优化的梯度超材料用于机械能限制和放大的强化学习方法。通过邻近策略优化算法，训练增强代理以最佳地设置谐振器阵列的长度和间距。设计优化问题是正式的马尔可夫决策问题，通过分裂成一个离散的决策数的优化过程。作为由局部共振的空间分布支配的梯度超材料的物理，可能的配置的空间通过使用用于共振器布置的连续函数来约束。已进行了初步的分析调查，通过处理它作为一个局部共振系统的分析系统的色散特性。优化过程的结果证实了以前的调查结果，突出了所提出的方法的有效性和鲁棒性的梯度谐振器的系统时，用于机械能限制和放大。谐振器间距的作用被示出为相对于谐振器长度是次要的，或者换句话说，相对于谐振器的振荡频率是次要的。然而，还证明了减少谐振器的数量可能是有利的。还由于分析持续时间的自适应控制，与谐振器长度和间隔的联合优化相关的结果通过几乎唯一地在扩大采集器振荡发生的时间而不放大这些振荡的情况下工作，显著地克服了先前已知系统的性能。所提出的程序是适合于应用到广泛的设计优化问题，其中的设计选择的效果可以通过数值模拟进行评估。
英文摘要：
A reinforcement learning approach to design optimised graded metamaterials for mechanical energy confinement and amplification is described. Through the proximal policy optimisation algorithm, the reinforcement agent is trained to optimally set the lengths and the spacing of an array of resonators. The design optimisation problem is formalised in a Markov decision problem by splitting the optimisation procedure into a discrete number of decisions. Being the physics of graded metamaterials governed by the spatial distribution of local resonances, the space of possible configurations is constrained by using a continuous function for the resonators arrangement. A preliminary analytical investigation has been performed to characterise the dispersive properties of the analysed system by treating it as a locally resonant system. The outcomes of the optimisation procedure confirms the results of previous investigations, highlighting both the validity of the proposed approach and the robustness of the systems of graded resonators when employed for mechanical energy confinement and amplification. The role of the resonator spacing is shown to be secondary with respect to the resonator lengths or, in other words, with respect to the oscillation frequencies of the resonators. However, it is also demonstrated that reducing the number of resonators can be advantageous. The outcomes related to the joint optimisation of the resonator lengths and spacing, thanks also to the adaptive control of the analysis duration, overcome significantly the performance of previously known systems by working almost uniquely on enlarging the time in which the harvester oscillations take place without amplifying these oscillations. The proposed procedure is suitable to be applied to a wide range of design optimisation problems in which the effect of the design choices can be assessed through numerical simulations.
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