Time difference detection based on sliding window all-phase FFT and Kalman filtering for precise flow measurement.

Coriolis mass flowmeter (CMF) measures the mass flow rate by detecting the time difference, typically using frequency domain methods. However, the spectrum leakage is the primary challenge. To address this issue, a new time difference detection method is proposed utilizing sliding window and all-phase fast Fourier transform. The computational complexity is reduced considering the changes in signal frequency. To further improve the stability and response speed of the measured value, a Kalman filtering algorithm based on variance detection is also proposed for post-processing. A transmitter system is developed to validate the proposed methods. The results demonstrate that, for single phase fluids, the accuracy is better than 0.5‰ and the repeatability is better than 0.2‰, thereby offering an improvement in the accuracy of CMF and supporting for industrial applications.

High-sensitivity fiber optic graphene resonant accelerometer.

This study proposes a high-sensitivity resonant graphene accelerometer based on a pressure-induced sensing mechanism. The accelerometer design encompasses an optical fiber and a vacuum-sealed graphene resonator affixed to a silicon sensitive film, incorporating a proof mass. This indirect sensing mechanism effectively mitigates the vibration mode aliasing of graphene and the proof mass while ensuring a minimal energy loss in the operating resonator. The mechanical vibration of graphene is excited and detected through an all-fiber optical system. Notably, the proposed sensor demonstrates a sensitivity of 34.3 kHz/g within the range of 0-3.5 g, which is eight times higher than comparable accelerometers utilizing a proof mass on a graphene membrane. This work exhibits a novel, to the best of our knowledge, approach to an acceleration measurement using 2D resonators, exhibiting distinct advantages in terms of compact size and heightened sensitivity.

Ultrasensitive Acoustic Detection Using an Enlarged Fabry-Perot Cavity with a Graphene Diaphragm.

For exerting high sensitivity of ultrathin graphene to detection deformation, an enlarged backing air cavity (EBC) structure is developed to further enhance the mechanical sensitivity (SM) of a graphene-based Fabry-Perot (F-P) acoustic sensor. COMSOL acoustic field simulation on the air cavity size-dependent SM confirms the optimal length and radius of the EBC of 0.2 and 1.5 mm, respectively, with the maximum simulation SM of 26.16 nm/Pa@1 kHz. Acoustic experiments further demonstrate that the frequency response of the fabricated graphene-based F-P acoustic sensor after the use of the EBC is enhanced by 5.73-79.33 times in the range of 0.5-18 kHz, compared with the conventional one without the EBC. Especially the maximum SM is up to 187.32 nm/Pa@16 kHz, which is at least 17% higher than the SM values ranging from 1.1 to 160 nm/Pa in previously reported F-P acoustic sensors using various diaphragm materials. More acoustic characteristics are examined to highlight various merits of the EBC structure, including a signal-to-noise ratio (SNR) of 60-75 dB@0.5-18 kHz, a time stability of less than ±1.3% for 90 min, a detection resolution of 0.01 Hz, and a high-fidelity speech detection with a cross-correlation coefficient of greater than 0.9, thereby revealing its high-performance weak acoustic sensing and speech recognition applications.

High-Sensitivity Graphene MOEMS Resonant Pressure Sensor.

Nanomechanical resonators made from suspended graphene exhibit high sensitivity toward pressure variations. Nevertheless, these devices exhibit significant energy loss in nonvacuum environments due to air damping, as well as inevitably weak gas leakage within the reference cavity because of the slight permeation of graphene. We present a new type of graphene resonant pressure sensor utilizing micro-opto-electro-mechanical systems technology, which features a multilayer graphene membrane that is sealed in vacuum and adhered to pressure-sensitive silicon film with grooves. This approach innovatively employs an indirectly sensitive method, exhibiting 60 times smaller energy loss in atmosphere, and solving the long-standing issue of gas permeation between the substrate and graphene. Notably, the proposed sensor exhibits a high pressure sensitivity of 1.7 Hz/Pa, which is 5 times higher than the sensitivity of the silicon counterparts. Also, the all-optical encapsulating cavity structure contributes a high signal-to-noise ratio of 6.9 × 10-5 Pa-1 and a low temperature drift (0.014%/◦C). The proposed method offers a promising solution for long-term stability and energy loss suppression of pressure sensors using two-dimensional materials as the sensitive membrane.

The Effect of Annealing and Optical Radiation Treatment on Graphene Resonators.

Graphene resonant sensors have shown strong competitiveness with respect to sensitivity and size. To advance the applications of graphene resonant sensors, the damage behaviors of graphene harmonic oscillators after thermal annealing and laser irradiation were investigated by morphology analysis and frequency domain vibration characteristics. The interface stress was proven to be the key factor that directly affected the yield of resonators. The resulting phenomenon could be improved by appropriately controlling the annealing temperature and size of resonators, thereby achieving membrane intactness of up to 96.4%. However, micro-cracks were found on the graphene sheets when continuous wave (CW) laser power was more than 4 mW. Moreover, the fluctuating light energy would also cause mechanical fatigue in addition to the photothermal effect, and the threshold damage power for the sinusoidally modulated laser was merely 2 mW. In this way, based on the amplitude-frequency surface morphology of the graphene resonator, the thermal time constant of the order of a few microseconds was confirmed to evaluate the damage of the graphene oscillator in situ and in real time, which could be further extended for those resonators using other 2D materials.

Research Progress of Graphene Nano-Electromechanical Resonant Sensors-A Review.

Graphene nano-electromechanical resonant sensors have wide application in areas such as seawater desalination, new energy, biotechnology, and aerospace due to their small size, light weight, and high sensitivity and resolution. This review first introduces the physical and chemical properties of graphene and the research progress of four preparation processes of graphene. Next, the principle prototype of graphene resonators is analyzed, and three main methods for analyzing the vibration characteristics of a graphene resonant sheet are described: molecular structural mechanics, non-local elastic theory and molecular dynamics. Then, this paper reviews research on graphene resonator preparation, discussing the working mechanism and research status of the development of graphene resonant mass sensors, pressure sensors and inertial sensors. Finally, the difficulties in developing graphene nano-electromechanical resonant sensors are outlined and the future trend of these sensors is described.

An Ultrahigh-Sensitivity Graphene Resonant Gyroscope.

In this study, a graphene beam was selected as a sensing element and used to form a graphene resonant gyroscope structure with direct frequency output and ultrahigh sensitivity. The structure of the graphene resonator gyroscope was simulated using the ANSYS finite element software, and the influence of the length, width, and thickness of the graphene resonant beam on the angular velocity sensitivity was studied. The simulation results show that the resonant frequency of the graphene resonant beam decreased with increasing the beam length and thickness, while the width had a negligible effect. The fundamental frequency of the designed graphene resonator gyroscope was more than 20 MHz, and the sensitivity of the angular velocity was able to reach 22,990 Hz/°/h. This work is of great significance for applications in environments that require high sensitivity to extremely weak angular velocity variation.

Optical-Thermally Excited Graphene Resonant Mass Detection: A Molecular Dynamics Analysis.

In consideration of the presented optical-thermally excited resonant mass detection scheme, molecular dynamics calculations are performed to investigate the thermal actuation and resonant mass sensing mechanism. The simulation results indicate that an extremely high temperature exists in a 6% central area of the graphene sheet exposed to the exciting laser. Therefore, constraining the laser driving power and enlarging the laser spot radius are essential to weaken the overheating in the middle of the graphene sheet, thus avoiding being burned through. Moreover, molecular dynamics calculations demonstrate a mass sensitivity of 214 kHz/zg for the graphene resonator with a pre-stress of 1 GPa. However, the adsorbed mass would degrade the resonant quality factor from 236 to 193. In comparison, the sensitivity and quality factor could rise by 1.3 and 4 times, respectively, for the graphene sheet with a pre-stress of 5 GPa, thus revealing the availability of enlarging pre-stress for better mass sensing performance.

Hollow-core fiber photothermal methane sensor with temperature compensation.

We demonstrate a high sensitivity all-fiber spectroscopic methane sensor based on photothermal interferometry. With a 2.4-m-long anti-resonant hollow-core fiber, a 1654 nm distributed feedback laser, and a Raman fiber amplifier, a noise-equivalent concentration of ${\sim}{4.3}\;{\rm ppb}$ methane is achieved at the room temperature and pressure of ${\sim}{1}\;{\rm bar}$. The effects of temperature on the photothermal phase modulation as well as the stability of the interferometer are studied. By introducing a temperature-dependent compensation factor and stabilizing the interferometer at quadrature, signal instability of ${\sim}{2.1}\%$ is demonstrated for temperature variation from 296 to 373 K.

A Deep Learning-Based Automatic First-Arrival Picking Method for Ultrasound Sound-Speed Tomography.

Ultrasound sound-speed tomography (USST) has shown great prospects for breast cancer diagnosis due to its advantages of nonradiation, low cost, 3-D breast images, and quantitative indicators. However, the reconstruction quality of USST is highly dependent on the first-arrival picking of the transmission wave. Traditional first-arrival picking methods have low accuracy and noise robustness. To improve the accuracy and robustness, we introduced a self-attention mechanism into the bidirectional long short-term memory (BLSTM) network and proposed the self-attention BLSTM (SAT-BLSTM) network. The proposed method predicts the probability of the first-arrival time and selects the time with maximum probability. A numerical simulation and prototype experiment were conducted. In the numerical simulation, the proposed SAT-BLSTM showed the best results. For signal-to-noise ratios (SNRs) of 50, 30, and 15 dB, the mean absolute errors (MAEs) were 48, 49, and 76 ns, respectively. The BLSTM had the second-best results, with MAEs of 55, 56, and 85 ns, respectively. The MAEs of the Akaike information criterion (AIC) method were 57, 296, and 489 ns, respectively. In the prototype experiment, the MAEs of the SAT-BLSTM, the BLSTM, and the AIC were 94, 111, and 410 ns, respectively.

The Effect of Edge Mode on Mass Sensing for Strained Graphene Resonators.

Edge mode could disturb the ultra-subtle mass detection for graphene resonators. Herein, classical molecular dynamics simulations are performed to investigate the effect of edge mode on mass sensing for a doubly clamped strained graphene resonator. Compared with the fundamental mode, the localized vibration of edge mode shows a lower frequency with a constant frequency gap of 32.6 GHz, despite the mutable inner stress ranging from 10 to 50 GPa. Furthermore, the resonant frequency of edge mode is found to be insensitive to centrally located adsorbed mass, while the frequency of the fundamental mode decreases linearly with increasing adsorbates. Thus, a mass determination method using the difference of these two modes is proposed to reduce interferences for robust mass measurement. Moreover, molecular dynamics simulations demonstrate that a stronger prestress or a higher width-length ratio of about 0.8 could increase the low-quality factor induced by edge mode, thus improving the performance in mass sensing for graphene resonators.

Synchronization Theory-Based Analysis of Coupled Vibrations of Dual-Tube Coriolis Mass Flowmeters.

Certain nonlinear influences are found in dual-tube Coriolis mass flowmeters (CMFs). According to experimentation, a nonlinearity dominated by frequency-doubling signals can be observed in the measuring signal. In general, such nonlinear effects are simplified as linear systems or neglected through processing. In this paper, a simplified model has been constructed for dual-beam CMFs based on the theory of nonlinear dynamics, with the spring-damper system as the medium for the dual-beam coupled vibrations. Next, the dynamics differential equation of the coupled vibrations is set up on the basis of the Lagrangian equation. Furthermore, numerical solutions are obtained using the Runge-Kutta fourth-order method. The study then fits discrete points of the numerical solutions, which are converted into the frequency domain to observe the existence of frequency-doubling signal components. Our findings show that frequency-doubling components exist in the spectrogram, proving that these nonlinear influences are a result of the motions of coupled vibrations. In this study, non-linear frequency-doubling signal sources are qualitatively analyzed to formulate a theoretical basis for CMFs design.

Gas sensing with mode-phase-difference photothermal spectroscopy assisted by a long period grating in a dual-mode negative-curvature hollow-core optical fiber.

We demonstrate sensitive gas detection with mode-phase-difference photothermal spectroscopy assisted by a long period grating (LPG) inscribed on a dual-mode negative-curvature hollow-core fiber (NC-HCF). The LPG is inscribed using a pulsed CO2 laser, which enables pump propagation in the fundamental LP01 mode to achieve maximum photothermal phase modulation while exciting both the LP01 and LP11 modes at the probe wavelength to form a dual-mode interferometer for detection of the phase difference. With a 1533 nm pump and a 1620 nm probe, a noise equivalent concentration of ∼2.2 ppb acetylene is achieved with an 85-cm-long NC-HCF gas cell and 1 s lock-in time constant.

Application of principal component analysis method for micro-resonator weak resonant signal detection.

The characteristic of weak resonant signal output by an electrothermally excited microresonator is analyzed, and the principal component analysis (PCA) method is proposed and applied in the resonant frequency detection of the output weak signal by separating the noises. Simulation on weak resonant signals under different levels of noises and different quality factors of the resonator was conducted after the influence of the data selection window width and the principal component number on detection results was analyzed. Finally, the experiment platform was built, and the output signal of the sensor sample was used to verify the detection effect of the proposed PCA method. Simulation and experiment results show that the proposed PCA method could accurately obtain the resonant frequency compared with the resonant frequency obtained by the smoothing filter and Lorentzian fitting method.

Mode-phase-difference photothermal spectroscopy for gas detection with an anti-resonant hollow-core optical fiber.

Laser spectroscopy outperforms electrochemical and semiconductor gas sensors in selectivity and environmental survivability. However, the performance of the state-of-the-art laser sensors is still insufficient for many high precision applications. Here, we report mode-phase-difference photothermal spectroscopy with a dual-mode anti-resonant hollow-core optical fiber and demonstrate all-fiber gas (acetylene) detection down to ppt (parts-per-trillion) and <1% instability over a period of 3 hours. An anti-resonant hollow-core fiber could be designed to transmit light signals over a broad wavelength range from visible to infrared, covering molecular absorption lines of many important gases. This would enable multi-component gas detection with a single sensing element and pave the way for ultra-precision gas sensing for medical, environmental and industrial applications.

A phase difference measurement method based on strong tracking filter for Coriolis mass flowmeter.

In order to improve the measurement accuracy of Coriolis mass flowmeters, this paper investigates the possible application of a strong tracking filter during signal processing. Specifically, a novel phase difference measurement method, based on a strong tracking filter for Coriolis mass flowmeters, is proposed in order to overcome the problems associated with the extended Kalman filters, which cannot accurately track time-varying phase differences. Compared with the existing methods, the proposed method can continuously track phase difference variation with high precision. The proposed method is a parallel algorithm that does not need to predict signal frequency in advance; this can effectively eliminate the quadratic error associated with frequency estimation. The results of simulation and experiments verify the proposed method that has better estimation performance and enhances the anti-interference performance of phase difference estimation, which contributes to improving the measurement accuracy of Coriolis mass flowmeters.

Stress-Insensitive Resonant Graphene Mass Sensing via Frequency Ratio.

Herein, a peripherally clamped stretched square monolayer graphene sheet with a side length of 10 nm was demonstrated as a resonator for atomic-scale mass sensing via molecular dynamics (MD) simulation. Then, a novel method of mass determination using the first three resonant modes (mode11, mode21 and mode22) was developed to avoid the disturbance of stress fluctuation in graphene. MD simulation results indicate that improving the prestress in stretched graphene increases the sensitivity significantly. Unfortunately, it is difficult to determine the mass accurately by the stress-reliant fundamental frequency shift. However, the absorbed mass in the middle of graphene sheets decreases the resonant frequency of mode11 dramatically while having negligible effect on that of mode21 and mode22, which implies that the latter two frequency modes are appropriate for compensating the stress-induced frequency shift of mode11. Hence, the absorbed mass, with a resolution of 3.3 × 10-22 g, is found using the frequency ratio of mode11 to mode21 or mode22, despite the unstable prestress ranging from 32 GPa to 47 GPa. This stress insensitivity contributes to the applicability of the graphene-based resonant mass sensor in real applications.

Opto-thermally Excited Fabry-Perot Resonance Frequency Behaviors of Clamped Circular Graphene Membrane.

An opto-thermally excited optical fiber Fabry-Perot (F-P) resonant probe with suspended clamped circular graphene diaphragm is presented in this paper. Then, the dependence of resonance frequency behaviors of graphene diaphragm upon opto-mechanical factors including membrane properties, laser excitation parameters and film boundary conditions are investigated via COMSOL Multiphysics simulation. The results show that the radius and thickness of membrane will linearly affect the optical fiber light-induced temperature distribution, thus resulting in rapidly decreasing resonance frequency changes with the radius-to-thickness ratio. Moreover, the prestress can be regulated in the range of 108 Pa to 108 Pa by altering the environmental temperature with a scale factor of 14.2 MPa/K. It is important to note that the availability of F-P resonant probe with a defective clamped circular graphene membrane can be improved notably by fabricating the defected circular membrane to a double-end clamped beam, which gives a broader perspective to characterize the resonance performance of opto-thermally excited F-P resonators.

Ultrafast miniature fiber-tip Fabry-Perot humidity sensor with thin graphene oxide diaphragm.

We demonstrate here an ultrafast, miniature, and high-performance fiber-tip Fabry-Perot (F-P) humidity sensor with ∼300 nm-thick graphene oxide (GO) diaphragm suspended onto the end face of a capillary tube with an inner diameter of 50 µm and a cavity length of ∼100 µm. The sensitivity to relative humidity (RH) spanning from ∼10%RH to ∼90%RH was examined based on the wavelength shift in the interference spectrum. Due to the intrinsic hydrophilicity of the porous GO membrane, the developed sensor exhibited an average wavelength variation of ∼0.2 nm/%RH, which indicated a relatively broad and readily detectable RH linear measurement range. More prominently, an ultrahigh response time of 60 ms was achieved over other alternative F-P humidity sensors previously reported, to our knowledge.

Modeling and Analysis of a Novel Ultrasensitive Differential Resonant Graphene Micro-Accelerometer with Wide Measurement Range.

A novel, ultrahigh-sensitivity wide-range resonant micro-accelerometer using two differential double-clamped monolayer graphene beams is designed and investigated by steady-state simulation via COMSOL Multiphysics software in this paper. Along with stiffness-enhanced optimized folded support beams, two symmetrical 3-GPa prestressed graphene nano-beams serve as resonant sensitive elements with a size of 10 µm × 1 µm (length × width) to increase the acceleration sensitivity while extending the measurement range. The simulation results show that the accelerometer with cascade-connected graphene and proof-mass assembly exhibits the ultrahigh sensitivity of 21,224 Hz/g and quality factor of 9773 in the range of 0⁻1000 g. This is remarkably superior to previously reported studies characterized by attaching proof mass to the graphene components directly. The proposed accelerometer shows great potential as an alternative to quartz and silicon-based resonant sensors in high-impact and highly sensitive inertial measurement applications.