“…In principle, a discrete action space could have been set by modifying the length of each resonator according to the tolerances of the manufacturing process. However, considering 30 resonators and a fabrication process tolerance of 0.15 m (consistent with the STMicroelectronics ThELMA®technology 42 ) leads to an exploding number of possible designs. Consequently, a continuous action space and a continuous system state have been preferred, and the use of function approximators, namely NNs, is required instead of tabular approaches.…”
Section: Methodsmentioning
confidence: 99%
“…On the application side, the optimisation of graded metamaterials for energy harvesting under a realistic input has been considered for the first time. The design we propose is fully compatible with micro fabrication paving a path towards the development of ultra-wide band (UWB) micro-electro-mechanical systems (MEMS) 42 for energy harvesting using metamaterials. Figure 1 Schematic of the device used for energy harvesting and the optimisation procedure.…”
The energy harvesting capability of a graded metamaterial is maximised via reinforcement learning (RL) under realistic excitations at the microscale. The metamaterial consists of a waveguide with a set of beam-like resonators of variable length, with piezoelectric patches, attached to it. The piezo-mechanical system is modelled through equivalent lumped parameters determined via a general impedance analysis. Realistic conditions are mimicked by considering either magnetic loading or random excitations, the latter scenario requiring the enhancement of the harvesting capability for a class of forcing terms with similar but different frequency content. The RL-based optimisation is empowered by using the physical understanding of wave propagation in a such local resonance system to constrain the state representation and the action space. The procedure outcomes are compared against grading rules optimised through genetic algorithms. While genetic algorithms are more effective in the deterministic setting featuring the application of magnetic loading, the proposed RL-based proves superior in the inherently stochastic setting of the random excitation scenario.
“…In principle, a discrete action space could have been set by modifying the length of each resonator according to the tolerances of the manufacturing process. However, considering 30 resonators and a fabrication process tolerance of 0.15 m (consistent with the STMicroelectronics ThELMA®technology 42 ) leads to an exploding number of possible designs. Consequently, a continuous action space and a continuous system state have been preferred, and the use of function approximators, namely NNs, is required instead of tabular approaches.…”
Section: Methodsmentioning
confidence: 99%
“…On the application side, the optimisation of graded metamaterials for energy harvesting under a realistic input has been considered for the first time. The design we propose is fully compatible with micro fabrication paving a path towards the development of ultra-wide band (UWB) micro-electro-mechanical systems (MEMS) 42 for energy harvesting using metamaterials. Figure 1 Schematic of the device used for energy harvesting and the optimisation procedure.…”
The energy harvesting capability of a graded metamaterial is maximised via reinforcement learning (RL) under realistic excitations at the microscale. The metamaterial consists of a waveguide with a set of beam-like resonators of variable length, with piezoelectric patches, attached to it. The piezo-mechanical system is modelled through equivalent lumped parameters determined via a general impedance analysis. Realistic conditions are mimicked by considering either magnetic loading or random excitations, the latter scenario requiring the enhancement of the harvesting capability for a class of forcing terms with similar but different frequency content. The RL-based optimisation is empowered by using the physical understanding of wave propagation in a such local resonance system to constrain the state representation and the action space. The procedure outcomes are compared against grading rules optimised through genetic algorithms. While genetic algorithms are more effective in the deterministic setting featuring the application of magnetic loading, the proposed RL-based proves superior in the inherently stochastic setting of the random excitation scenario.
“…MEMSs are often constituted by standard structural elements such as (micro)beams, (micro)plates and micro(arches) suspended over a parallel ground plate, and under direct current (DC) voltage, alternating current (AC) voltage, or both, and classical theories usually apply [6]. Recent review papers present the current stage of research on electrically actuated MEMS, analyzing their theoretical developments and mathematical modeling, nonlinear static and dynamic behaviors, advances in fabrication technologies, development of highperformance nano and microscale systems, and other recent advances in the field [7][8][9][10][11][12].…”
This work aims to study the effect of uncertainties and noise on the nonlinear global dynamics of a micro-electro-mechanical arch obtained from an imperfect microbeam under an axial load and electric excitation. An adaptative phase-space discretization strategy based on an operator approach is proposed. The Ulam method, a classical discretization of flows in phase-space, is extended here to nondeterministic cases. A unified description is formulated based on the Perron-Frobenius, Koopman, and Foias linear operators. Also, a procedure to obtain global structures in the mean sense of systems with parametric uncertainties is presented. The stochastic basins of attraction and attractors’ distributions replace the usual basin and attractor concepts. For parameter uncertainty cases, the phase-space is augmented with the corresponding probability space. The microarch is assumed to be shallow and modelled using a nonlinear Bernoulli-Euler beam theory and is discretized by the Galerkin method using as interpolating function the linear vibration modes. Then, from the discretized multi degree of freedom model (mdof) model, an accurate single degree of freedom (sdof) reduced order model, based on theory of nonlinear normal modes, is derived. Several competing attractors are observed, leading to different (acceptable or unacceptable) behaviours. Extensive numerical simulations are performed to investigate the effect of noise and uncertainties on the coexisting basins of attraction, attractors` distributions, and basins boundaries. The appearance and disappearance of attractors and stochastic bifurcation are observed, and the time-dependency of stochastic responses is demonstrated, with long-transients influencing global behaviour. To consider uncertainties and noise in design, a dynamic integrity measure is proposed via curves of constant probability, which give quantitative information about the changes in structural safety. For each attractor, the basin robustness as a function of a stochastic parameter is investigated. The weighted basin area can quantify the integrity of nondeterministic cases, being also the most natural generalization of the global integrity measure. While referring to particular MEMS, the relevance of the dynamical integrity analysis for stochastic systems to quantify tolerances and safety margins is underlined here.
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