Real-time stochastic response analysis as a tool for monitoring cantilever mechanical properties ☆

Abstract Microcantilever-based sensors are very promising devices for biochemical applications. They are usually operated in two modes. In the first one, a microcantilever static bending induced by the surface stress is observed. In the second mode, resonant frequency shift caused by mass loading is measured. The second mode requires an external force to excite cantilever vibrations. There is a possibility to use a stochastic excitation signal to estimate frequency shift as well as other interesting mechanical properties, such as effective spring constant or damping. Cantilever thermal self-vibrations or artificially generated white noise are very convenient examples of such a stochastic excitation signal. In the paper a real-time stochastic response analysis (RTSA) technique is presented. It is based on autoregressive moving average (ARMA) process modeling. Estimated model parameters are used for calculation of the eigenfrequency, quality factor and effective spring constant of a given vibration mode. The description of the entire procedure is presented, along with the results of simulations. The results confirm validity of the proposed ARMA model and show expected estimation errors for an illustrative set of cantilevers. The proposed algorithm is also applied to monitor the quality factor and resonant frequency of an electromagnetically-actuated microcantilever. The stochastic signal used to excite the cantilever is generated by a very simple white noise generator. The RTSA enables simultaneous monitoring of the cantilever resonant frequency and quality factor. The proposed solution is an interesting option in applications, in which simplicity and cost of the measurement system are key issues.