In-Plane and Out-of-Plane 2-D Microdisplacement Sensor Based on a Single Microwave Resonator With Machine Learning

Microwave displacement sensors have garnered significant research interest in recent years and have found successful applications in industrial automation and aerospace engineering. However, most microwave sensors are limited to measuring in-plane displacement, with the assumption that out-of-plane displacement remains constant during operation. In this work, we propose and experimentally demonstrate a novel concept for 2-D microdisplacement sensing that simultaneously measures both in-plane and out-of-plane displacement. We developed a proof-of-concept sensor system based on a custom-made coaxial cable resonator (CCR) serving as the stator and a rubber-metal heterogeneous plate as the movable part. The in-plane and out-of-plane micromovements of the plate relative to the CCR’s open-end plane were successfully detected by monitoring the fundamental resonant frequency of the CCR. Additionally, machine learning-based analysis was employed to decouple the CCR’s responses to the 2-D displacement, enabling independent and accurate quantification of both in-plane and out-of-plane displacements. Our strategy combines the heterogeneous plate, which adds spatial information, with machine learning analysis for response decoupling, thereby paving the way for the development of multidimensional sensing systems using a simple 1-D sensor device. The resulting 2-D displacement sensor has the potential to be extended for measuring other 2-D physical and mechanical parameters, such as vibration and acceleration.