Highly sensitive mass sensing using data-driven iterative learning of resonator dynamics

Mass sensing using mode localization in weakly coupled, otherwise identical resonators has been proposed in the past due to its high sensitivity. In practice, owing to limited machining accuracy, such ideal operating conditions are difficult to achieve and sensitivity is significantly reduced relative to theoretical predictions. To overcome such limitations, previous work by the second author proposed a hybrid realization, in which one of the resonators is replaced with a computational model that is virtually coupled with the remaining physical resonator in real time. While such real-time computation and coupling may be viable in macro-scale devices, in micro- and nano-scale resonators with much higher natural frequency, real-time coupling cannot be adopted because extremely fast calculations are required. In addition, at any scale, uncertain communication delays and unmodeled actuator dynamics contribute to further deviations from ideal conditions. To avoid real-time computation and minimize the effects of delays and actuator dynamics, past work by the third author developed a concept where the responses of weakly coupled physical and virtual resonators are learned through data-driven application of an iterative root-finding algorithm without any real-time coupling. In this paper, we demonstrate through experiments a practical mass sensing algorithm based on this data-driven approach applied to a linear beam resonator and a virtual self-excited van der Pol oscillator. We show that mass added to the beam resonator may be measured experimentally without real-time computation or coupling to the virtual resonator, and with high sensitivity that is tunable using parameters of the computational model.