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Abstract Reservoir computing (RC) is a bio-inspired neural network structure which can be implemented in hardware with ease. It has been applied across various fields such as memristors, and electrochemical reactions, among which the micro-electro-mechanical systems (MEMS) is supposed to be the closest to sensing and computing integration. While previous MEMS RCs have demonstrated their potential as reservoirs, the amplitude modulation mode was found to be inadequate for computing directly upon sensing. To achieve this objective, this paper introduces a novel MEMS reservoir computing system based on stiffness modulation, where natural signals directly influence the system stiffness as input. Under this innovative concept, information can be processed locally without the need for advanced data collection and pre-processing. We present an integrated RC system characterized by small volume and low power consumption, eliminating complicated setups in traditional MEMS RC for data discretization and transduction. Both simulation and experiment were conducted on our accelerometer. We performed nonlinearity tuning for the resonator and optimized the post-processing algorithm by introducing a digital mask operator. Consequently, our MEMS RC is capable of both classification and forecasting, surpassing the capabilities of our previous non-delay-based architecture. Our method successfully processed word classification, with a 99.8% accuracy, and chaos forecasting, with a 0.0305 normalized mean square error (NMSE), demonstrating its adaptability for multi-scene data processing. This work is essential as it presents a novel MEMS RC with stiffness modulation, offering a simplified, efficient approach to integrate sensing and computing. Our approach has initiated edge computing, enabling emergent applications in MEMS for local computations.

Abstract The development of mode-localized sensors based on amplitude output metrics has attracted increasing attention in recent years due to the potential of such sensors for high sensitivity and resolution. Mode-localization phenomena leverage the interaction between multiple coupled resonant modes to achieve enhanced performance, providing a promising solution to overcome the limitations of traditional sensing technologies. Amplitude noise plays a key role in determining the resolution of mode-localized sensors, as the output metric is derived from the measured AR (amplitude ratio) within the weakly coupled resonator system. However, the amplitude noise originating from the weakly coupled resonator’s closed-loop circuit has not yet been fully investigated. This paper presents a decouple-decomposition (DD) noise analysis model, which is applied to achieve high resolution in a mode-localized tilt sensor based on a weakly coupled resonator closed-loop circuit. The DD noise model separates the weakly coupled resonators using the decoupling method considering the nonlinearity of the resonators. By integrating the decoupled weakly coupled resonators, the model decomposes the weakly coupled resonator’s closed-loop circuit into distinct paths for amplitude and phase noise analyses. The DD noise model reveals noise effects at various circuit nodes and models the system noise in the closed-loop circuit of the weakly coupled resonators. MATLAB/Simulink simulations verify the model’s accuracy when compared to theoretical analysis. At the optimal operating point, the mode-localized tilt sensor achieves an input-referred instability of 3.91 × 10-4° and an input-referred AR of PSD of 2.01 × 10-4°⁄√Hz using the closed-loop noise model. This model is also applicable to other varieties of mode-localized sensors.

To mitigate the impact of low-frequency noise from the tunnel magnetoresistance (TMR) current sensor and ambient stray magnetic fields on weak current detection accuracy, we propose a high-resolution modulation-demodulation test method. This method modulates and demodulates the measurement signal, shifting low-frequency noise to the high-frequency band for effective filtering, thereby isolating the target signal from the noise. In this study, we developed a Simulink model for the TMR current sensor modulation-demodulation test method. Practical time-domain and frequency-domain tests of the developed high-resolution modulation-demodulation method revealed that the TMR current sensor exhibits a nonlinearity as low as 0.045%, an enhanced signal-to-noise ratio (SNR) of 77 dB, and a heightened resolution of 100 nA. The findings indicate that this modulation-demodulation test method effectively reduces the impact of low-frequency noise on TMR current sensors and can be extended to other types of resistive devices.

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.

Abstract Reservoir computing is a potential neuromorphic paradigm for promoting future disruptive applications in the era of the Internet of Things, owing to its well-known low training cost and compatibility with hardware. It has been successfully implemented by injecting an input signal into a spatially extended reservoir of nonlinear nodes or a temporally extended reservoir of a delayed feedback system to perform temporal information processing. Here we propose a novel nondelay-based reservoir computer using only a single micromechanical resonator with hybrid nonlinear dynamics that removes the usually required delayed feedback loop. The hybrid nonlinear dynamics of the resonator comprise a transient nonlinear response, and a Duffing nonlinear response is first used for reservoir computing. Due to the richness of this nonlinearity, the usually required delayed feedback loop can be omitted. To further simplify and improve the efficiency of reservoir computing, a self-masking process is utilized in our novel reservoir computer. Specifically, we numerically and experimentally demonstrate its excellent performance, and our system achieves a high recognition accuracy of 93% on a handwritten digit recognition benchmark and a normalized mean square error of 0.051 in a nonlinear autoregressive moving average task, which reveals its memory capacity. Furthermore, it also achieves 97.17 ± 1% accuracy on an actual human motion gesture classification task constructed from a six-axis IMU sensor. These remarkable results verify the feasibility of our system and open up a new pathway for the hardware implementation of reservoir computing.

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.

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.

Accelerometers based on outputting amplitude ratios in weakly coupled resonators (WCRs) are attractive because their parametric sensitivity is higher by two or three orders of magnitudes than those based on outputting frequency. However, the impact of temperature on the coupler is a key factor in accelerometer applications. This paper proposed a novel mode-localized WCR accelerometer with a temperature compensation mechanism, with sensitive elements incorporating a double-ended tuning fork (DETF) resonator, clamped–clamped (CC) resonator, and a micro-lever coupler. The DETF out-of-phase mode is utilized, which is only sensitive to temperature, to measure the temperature change of WCRs and complete the temperature compensation using the compensation algorithm. This proposed method has no time delay in measuring the temperature of sensitive elements and no temperature difference caused by the uneven temperature field. The parametric sensitivity in amplitude ratio (AR) to acceleration drifting with temperature was theoretically analyzed, and the novel device was designed and fabricated by a silicon-on-glass process. Both simulation and experiment results demonstrated that the coupling stiffness drifted with temperature, which resulted in the drifts of its sensitivity to acceleration and zero-bias stability. Using the intrinsic mode of WCRs, in terms of the DETF out-of-phase mode, as an in situ thermometer and carrying out the temperature compensation algorithm, the drift of zero bias could be suppressed from 102 mg to 4.5 mg (g is the gravity acceleration), and the drift of the parameter sensitivity in AR was suppressed from 0.74 AR/g to 0.02 AR/g with the temperature range from 330 K to 370 K and acceleration range from 0 g to 0.2 g.

A mode-localized ΔE-effect magnetic sensor model is established theoretically and numerically. Based on the designed weakly coupled resonators with multi-layer film structure, it is investigated how the ΔE-effect of the magnetostrictive film under the external magnetic field causes the stiffness perturbation of the coupled resonators to induce the mode localization effect. Using the amplitude ratio (AR) as the output in the mode-localized ΔE-effect magnetic sensor can improve the relative sensitivity by three orders of magnitude compared with the traditional frequency output, which has been verified by simulations based on the finite element method (FEM). In addition, the effects of material properties and geometric dimensions on sensor performance parameters, such as sensitivity, linear range, and static operating point are also analyzed and studied in detail, providing the theoretical basis for the design and optimization of the mode-localized ΔE-effect magnetic sensor in different application scenarios. By reasonably optimizing the key parameters of the weekly coupled resonators, a mode-localized ΔE-effect magnetic sensor with the sensitivity of 18 AR/mT and a linear range of 0.8 mT can be achieved.

Mode-localized sensing paradigms applied to accelerometers have recently become popular research subjects. However, the output of mode-localized accelerometers is influenced by environment temperature due to the difference in the thermal properties of the coupling resonators and the temperature dependence of coupling stiffness. To improve the performance of mode-localized accelerometers against temperature, we proposed an in situ self-temperature compensation method by utilizing the resonant frequency besides of amplitude ratios, which can be implied online. Experimental results showed that there were nearly 79-times and 87-times improvement in zeros bias and scale factor, respectively.

Reservoir computing (RC) is a potential neuromorphic paradigm for physically realizing artificial intelligence systems in the Internet of Things society, owing to its well-known low training cost and compatibility with nonlinear devices. Micro-electro-mechanical system (MEMS) resonators exhibiting rich nonlinear dynamics and fading behaviors are promising candidates for high-performance hardware RC. Previously, we presented a non-delay-based RC using one single micromechanical resonator with hybrid nonlinear dynamics. Here, we innovatively introduce a nonlinear tuning strategy to analyze the computing properties (the processing speed and recognition accuracy) of the presented RC. Meanwhile, we numerically and experimentally analyze the influence of the hybrid nonlinear dynamics using the image classification task. Specifically, we study the transient nonlinear saturation phenomenon by fitting quality factors under different vacuums, as well as searching the optimal operating point (the edge of chaos) by the static bifurcation analysis and dynamic vibration numerical models of the Duffing nonlinearity. Our results in the optimal operation conditions experimentally achieved a high classification accuracy of (93 ± 1)% and several times faster than previous work on the handwritten digits recognition benchmark, profit from the perfect high signal-to-noise ratios (quality factor) and the nonlinearity of the dynamical variables.

Resonant accelerometers are promising because of their wide dynamic range and long-term stability. With quasi-digital frequency output, the outputs of resonant accelerometers are less vulnerable to the noise from circuits and ambience. Differential structure is usually adopted in a resonant accelerometer to achieve higher sensitivity to acceleration and to reduce common noise at the same time. Ideally, a resonant accelerometer is only sensitive to external acceleration. However, temperature has a great impact on resonant accelerometers, causing unexcepted frequency drift. In order to cancel out the frequency drift caused by temperature change, an improved temperature compensation method for differential vibrating accelerometers without additional temperature sensors is presented in this paper. Experiment results demonstrate that the temperature sensitivity of the prototype sensor is reduced from 43.16 ppm/°C to 0.83 ppm/°C within the temperature range of −10 °C to 70 °C using the proposed method.

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.

Non-contact and non-destructive acceleration measurement is receiving considerable attention due to their low cost, flexibility, and simplicity of implementation, as well as their excellent performance in some emerging applications such as medical electronics applications, vibration monitoring, and some other special scenarios. In this paper, a visual accelerometer system based on laser speckle optical flow detection named Viaxl is proposed. Compared with the conventional non-contact acceleration measurement method based on a laser system, Viaxl has moderate and stable performance with the advantages of low cost and simplicity of implementation. Experiment results demonstrate that Viaxl, which consists of a commercial camera and a low-cost laser pointer, can achieve real-time, non-contact acceleration measurement, and confirm the basic system performance of Viaxl: a measurement nonlinearity better than 1.3%, up to 31 dB signal-to-noise ratio, and 1150 Hz theoretic bandwidth; this demonstrates the huge potential of Viaxl in a wide range of applications, and provides a new possible technical method for non-contact acceleration detection.

This paper presents a low noise, high resolution and large dynamic range capacitive readout circuit for Micro-Electromechanical System accelerometer applying to seismic exploration. In comparison to conventional correlated double sampling structure, the proposed correlated double sampling structure is easier to realize, and the correlated double sampling capacitor in conventional structure is removed, also the number of switches is reduced to decrease switch thermal noise. The low frequency 1/f noise and offset voltage of op-amps are suppressed so as to improve resolution and increase dynamic range. The readout circuit chip has been fabricated using X-FAB 0.18-µm complementary metal-oxide-semiconductor technology, which measures 3.5mm2. Test results show that the capacitive resolution of the readout circuit is 2.5aF and the dynamic range reaches 127dB with a sampling frequency of 128 kHz. The readout circuit achieves a noise floor of -115 dBV / Hz at 100Hz with a sensitivity of 0.71mV/fF. [ABSTRACT FROM AUTHOR]