A Viscosity and Density Measurement Scheme Using Frequency and Quality Factor With an Error Compensation Approach

This article proposes a viscosity and density measurement scheme using resonant frequency and quality factor (Q-factor), with a deep learning (DL)-based error compensation approach. The scheme includes a viscosity and density decoupling algorithm based on a frequency response model capable of extracting resonant frequency and Q-factor of the first-order bending mode. A cantilever-based sensor prototype with glycerol–water mixtures at varying concentrations is prepared to validate the scheme’s effectiveness and comparative advantages. Compared to reference values obtained using a viscometer and densitometer, the highest relative errors in immersion measurements are 3.8% for viscosity and 0.9% for density. Relative to published works, the highest relative errors are decreased by 44.6% and 16.3% for viscosity and density, respectively. The experimentally verified numerical data are further used to construct error networks, with viscosity and density as features, and their respective decoupling errors serve as labels. Compared to decoupling values without compensation, the highest relative error in viscosity is reduced from 8% to 2%, representing a 75% decrease. Similarly, the highest relative error in density is significantly reduced from 3% to 0.7%, achieving a 76.67% decrease. The demonstrated effectiveness of the proposed scheme is expected to provide a new solution for designing high-accuracy cantilever-based resonant viscosity-density sensors.