Reduced Order Modeling of Nonlinear Vibrating Multiphysics Microstructures with Deep Learning-Based Approaches

Abstract

Micro-electro-mechanical-systems are complex structures, often involving nonlinearites of geometric and multiphysics nature, that are used as sensors and actuators in countless applications. Starting from full-order representations, we apply deep learning techniques to generate accurate, efficient, and real-time reduced order models to be used for the simulation and optimization of higher-level complex systems. We extensively test the reliability of the proposed procedures on micromirrors, arches, and gyroscopes, as well as displaying intricate dynamical evolutions such as internal resonances. In particular, we discuss the accuracy of the deep learning technique and its ability to replicate and converge to the invariant manifolds predicted using the recently developed direct parametrization approach that allows the extraction of the nonlinear normal modes of large finite element models. Finally, by addressing an electromechanical gyroscope, we show that the non-intrusive deep learning approach generalizes easily to complex multiphysics problems.

Jump and Pull-in Instability of a MEMS Gyroscope Vibrating System

“…Referring to it, we focus on the effect of the AC voltage frequency Ω and amplitude U da in the drive direction on the global dynamics of the micro gyroscope. Note that Y = ±d eg in Equation (2) shows the gap width between the proof mass and the upper or lower movable electrode of the detecting direction becoming zero, namely the pull-in of the micro gyroscope in the detecting direction. By introducing the following non-dimensional variables…”

“…Micromachined vibratory gyroscopes are typical MEMS inertia sensors used for the measurement of the angular velocities of carriers [ 1 , 2 ]. Their operation is based on energy transfer from the driving mode to its perpendicular vibrational mode, i.e., the detecting mode, due to Coriolis effect [ 3 ].…”

Modelling the Periodic Response of Micro-Electromechanical Systems through Deep Learning-Based Approaches

“…In nonlinear systems, like those emerging from the electromechanical modelling of MEMSs, the FRC is not a single-valued function of the forcing frequency ω, see Figure 4a. To overcome these difficulties, a possible solution is given by the approach proposed in [37], where instead of using the actuation frequency as an input parameter, this is replaced by a curvilinear abscissa that directly parametrises the FRC of interest. This additionally requires a model for the frequency value with respect to the other input parameters and the abscissa itself, see Figure 4b.…”

“…This compressed information represents a new coordinate system that allows reconstructing the full order problem with a decoder. This method has also been used to model micro-electromechanical systems (MEMSs) [36,37], demonstrating an excellent prediction ability. The application of deep learning-and general machine learning-based techniques may not be limited to MEMSs; they can also be retrieved, e.g., in real-time monitoring of sediment particles [38] or control in hydraulic fracturing [39][40][41].…”

“…MEMSs usually oscillate at resonance with a period imposed by an external excitation signal. The standard POD-DL-ROM can be used to model this steady state response by considering a time series of data representing a single period, as proposed for instance in [36,37]. However, this way of approaching the problem does not exploit its specific features and is not optimal.…”