Deep learning for simultaneous measurements of pressure and temperature using arch resonators

The ability to measure pressure and temperature using a MEMS sensor constitutes a major interest for several engineering applications. In this paper, we present a method and system for simultaneous measurements of pressure and temperature using electrically-actuated arch resonators. The sensor design is selected so that the arch microbeam is sensitive to temperature variations of the surrounding via the inherent thermal stress and to pressure change via the squeeze-film damping resulting from the air flow between the microbeam and the fixed underneath electrode (substrate). A physics-based model is formulated and validated by comparing the static deflection of the microbeam and its natural frequencies under varying temperature to experimental data reported in the literature. We use deep learning to estimate the pressure and temperature from the natural frequencies, quality factors and static deflection of the microbeam. Results show accurate prediction of the temperature and pressure from the quality factors of the arch resonator based on the first three vibration modes. Further improvement is achieved by adding the natural frequencies to the input data. The robustness of the deep learning approach to noise is demonstrated by the small errors obtained using different loss functions when introducing different noise levels to the training data. The proposed approach allows, for the first time, the combination of arch beams dynamics and deep learning techniques for simultaneous sensing of pressure and temperature.