Reservoir computing (RC) is an attractive paradigm of a recurrent neural network (RNN) architecture, owning to the ease of training and existing neuromorphic implementation. Its simulated performance matches other digital algorithms on a series of benchmarking tasks, such as prediction tasks and classification tasks. In this article, we propose a novel RC structure based on the coupled MEMS resonators with the enhanced dynamic richness to optimize the performance of the RC system both on the system level and data set level. Moreover, we first put forward that the dynamic richness of RC comprises linear dynamic richness and nonlinear dynamic richness, which can be enhanced by adding delayed feedbacks and nonlinear nodes, respectively. In order to set forth this point, we compare three typical RC structures, a single-nonlinearity RC structure with single-feedback, a single-nonlinearity RC structure with double-feedbacks, and the couple-nonlinearity RC structure with double-feedbacks. Specifically, four different tasks are enumerated to verify the performance of the three RC structures, and the results show the enhanced dynamic richness by adding delayed feedbacks and nonlinear nodes. These results prove that coupled MEMS resonators offer an interesting platform to implement a complex computing paradigm leveraging their rich dynamical features.

An MEMS resonant accelerometer is a temperature-sensitive device because temperature change affects the intrinsic resonant frequency of the inner silicon beam. Most classic temperature compensation methods, such as algorithm modeling and structure design, have large errors under rapid temperature changing due to the hysteresis of the temperature response of the accelerometer. To address this issue, we propose a novel reservoir computing (RC) structure based on a nonlinear silicon resonator, which is specifically improved for predicting dynamic information that is referred to as the input–output-improved reservoir computing (IOI-RC) algorithm. It combines the polynomial fitting with the RC on the input data mapping ensuring that the system always resides in the rich nonlinear state. Meanwhile, the output layer is also optimized by vector concatenation operation for higher memory capacity. Therefore, the new system has better performance in dynamic temperature compensation. In addition, the method is real-time, with easy hardware implementation that can be integrated with MEMS sensors. The experiment’s result showed a 93% improvement in IOI-RC compared to raw data in a temperature range of −20–60 °C. The study confirmed the feasibility of RC in realizing dynamic temperature compensation precisely, which provides a potential real-time online temperature compensation method and a sensor system with edge computing.

Due to the working principle of MEMS resonant accelerometers, their thermally induced frequency drift is an inevitable practical issue for their extensive application. This paper is focused on reducing the thermally induced packaging effects on the frequency drift. A leadless ceramic chip carrier package with a stress-buffering layer was proposed for a MEMS resonant accelerometer, and the influences of packaging structure parameters on the frequency drift were investigated through finite element simulations and verified experimentally. Because of the thermal mismatch between dissimilar materials, the thermo-mechanical stress within the resonant beam leads to a change in the effective stiffness and causes the frequency drift to decrease linearly with increasing temperature. Furthermore, our investigations reveal that increasing the stress-buffering layer thickness and reducing the solder layer thickness can significantly minimize the thermo-mechanical stress within the resonant beam. As the neutral plane approaches the horizontal symmetry plane of the resonant beam when optimizing the packaging structure, the effects of the compressive and tensile stresses on the effective stiffness of the resonant beam will cancel each other out, which can dramatically reduce the frequency drift. These findings provide guidelines for packaging design through which to improve the temperature stability of MEMS resonant accelerometers.

MEMS resonant accelerometers have attracted attention because of their high resolution and quasi-digital output, but their performances are seriously damaged by external temperature fluctuations. Our previous work proposed a Temperature-Drift Suppression Phase-Locked-Loop featuring a temperature-sensitive resonator (TSR) as a voltage-controlled oscillator to monitor the frequency variations of the accelerometer-sensitive resonator (ASR). To solve the problem of mismatched temperature coefficients between the TSR and ASR, the frequency synthesis unit is introduced in this paper. The temperature drift of the two resonators can offset each other by adjusting the division factor so that the acceleration drift caused by temperature can be mitigated. Additionally, the proposed SAFR algorithm automatically adjusts the locked range of the PLL, thereby expanding the full-scale range of the accelerometer. The effectiveness of the system is further validated through theoretical analysis and simulations. Experimental results indicate that the bias-instability is 3.7μg and the noise floor is 1.24μg/√Hz with ±2g full-scale range at room temperature. The temperature drift is 54mg within a temperature range of 10°C to 60°C which is reduced by 95% compared to the uncompressed MRA (1.23g).

This paper presents a scale factor calibration method based on virtual accelerations generated by electrostatic force. This method uses a series of voltage signals to simulate the inertial forces caused by the acceleration input, rather than frequent and laborious calibrations with high-precision instruments. The error transfer model of this method is systematically analyzed, and the geometrical parameters of this novel micromachined resonant accelerometer (MRA) are optimized. The experimental results demonstrate that, referring to the traditional earth’s gravitational field tumble calibration method, the error of the scale factor calibration is 0.46% within ±1 g by using our method. Moreover, the scale factor is compensated by virtual accelerations. After compensation, the maximum temperature drift of the scale factor decreases from 2.46 Hz/g to 1.02 Hz/g, with a temperature range from 40 °C to 80 °C.

This paper presents the theoretical analysis and experimental investigation of a weakly coupled resonant tilt sensor based on different output metrics, including mode frequency, amplitude ratio, amplitude difference, and eigenstate. Especially, we investigate the sensitivity, linear working range, stability, and noise analysis by theoretical analysis and evaluation of experimental results. The tilt sensor sensing element is the weakly coupled resonators, the output metrics of which shift is proportional to the effective stiffness perturbation caused by changes in input inertial force along the sensitive axis when any tilt angular is applied to the tilt sensor. Furthermore, it is demonstrated that there is an optimal operating point for amplitude difference output through theoretical analysis. The experimental results show that the minimum input-referred angle noise densities of the tilt sensor based on the amplitude ratio and amplitude difference are 1.03×10 ^-4 °/√Hz and 9.10×10 ^-5 °/√Hz, respectively. In addition, the weakly coupled resonant tilt sensor based on the amplitude ratio and amplitude difference outputs achieve resolutions of 9.79×10 ^-5 ° and 7.53×10 ^-5 ° with an integral time of 15s, and the mode frequency output achieves a resolution of 0.141×10 ^-5 ° with an integral time of 0.5s. The experimental results demonstrate that based on amplitude difference output has the best long-term stability and based on the mode frequency output has better short-term stability. Additionally, it is demonstrated that the output based on the amplitude ratio balances sensitivity, linear range, and long-term stability.