Machine-Learning Algorithm Models for Extracting the Inherent Resonance Frequency and Quality Factor of MEMS Resonators Under the Feed-Through Effect

As the basis of various micro-electromechanical system (MEMS) sensors and actuators, MEMS resonators are widely beset with the feed-through effect from parasitic capacitance networks, which makes it obstructive in directly acquiring the inherent resonance frequency and quality factor of a MEMS resonator from measured resonance responses. From the fresh perspective of resonance data modeling, we put forward machine-learning algorithm models to expediently extract these two critical indicators from resonance responses under varying-degree feed-through effects. First, the resonance datasets, which contain numerous feature data from amplitude-frequency responses and target data of the two critical indicators, are constructed with the equivalent circuit model. By introducing the dominance analysis based on the random forest (RF) algorithm, the heavy-weight parameters are selected from feature data and further serve as prediction evidence for cost-efficiently extracting the inherent resonance indicators. Then, based on the ~0.3-million-group datasets, two machine-learning algorithm models are trained with back-propagation (BP) neural networks for the two resonance indicators. Also, by optimizing hyperparameters in training, the test results from testing datasets manifest fine accuracy in extracting the resonance frequency (0.05%) and quality factor (0.71%) for the trained algorithm models. Finally, the experimental verification of trained algorithm models is implemented on a realistic MEMS resonator under four cases of feed-through effects, whose results indicate its low prediction errors of resonance frequency (<0.1%) and quality factor (<0.5%). In brief, the proposed algorithm models provide a novel strategy to accurately obtain inherent MEMS resonator indicators without any dependence on device structures, circuits, and operation conditions.