Frequency Lock Research Articles

Modulation of Phase-Locking Characteristics of NbOx Memristor by Ag Doping.

Memristors based on niobium oxide have attracted wide interest due to their applications in artificial neural network. Phase-locking (PL) characteristics of NbOx newly explored roots in complex nonlinear dynamics and exhibits great potential in periodical signal handling because of its bioinspired nature. In this study, we fabricate a Pd/Nb/Ag-NbOx/Nb/Pd memristive structure and study the effects of Ag doping on the PL characteristics. We clearly see that the NbOx memristor responds to signal in three distinct patterns. For the low-frequency input, the memristor fires spike series and locks the phase near during the positive period of sinusoidal input, and it encodes the input features by the spike number per period. For the middle-frequency input, the memristor fires one spike per period at a definite phase. The output has the same frequency as the input. The locked phase is proportional to the input frequency. For the high-frequency input, the memristor transforms high frequency to low frequency signal and locks at a definite phase higher than 2π. We combined the microstructural analysis and chaos dynamics to know that Ag doping will lower the activation energy, enhance the responding rate, and enhance thermal conductivity, which extends the locked frequency to 1.7 times the value of the undoped NbOx memristor. We also obtained the locked frequency of even 40 MHz after modulating the elementary circuit configuration according to the material modification and chaos model. Our study proposes to handle a signal with high efficiency resembling auditory sense and inspires a novel artificial intelligent computation prototype.

Reduction of vortex-induced vibrations of a cantilevered hydrofoil with passive piezoelectric shunt

This work first investigates the ability of a low order fluid-structure model to fit the vortex-induced vibrations (VIV) observed on a truncated hydrofoil in a hydrodynamic tunnel. A particular VIV area is scrutinized, for which a hydrodynamic excitation mechanism due to a Karman-type vortex wake organization successively locks the first torsional and second bending mode of the cantilevered hydrofoil. Coupling two structure oscillators with a Van der Pol wake oscillator satisfactorily reproduces the amplitude response and the lock-in frequency. In order to build a low order model allowing to optimize control strategy, a fourth degree of freedom corresponding to the electric circuit of a resonant piezoelectric shunt has been added. Composed of an inductance and a resistance connected to a piezoelectric patch, the passive shunt was tuned to minimize the vibration amplitude in the frequency lock-in range. Model predictions are finally compared with experimental results.

Flow field characteristics and vibration responses of saddle-shaped membrane structures

Elastically mounted flexible membrane roofs exposed to flows are prone to vortex-induced vibrations and even aero-instability due to the strong fluid–structure interaction (FSI). This study is to investigate the FSI mechanism in the saddle-shaped membrane structure over a range of Reynolds numbers and wind directions in laminar flows, by bridging structural vibration responses and flow dynamics. The aeroelastic characteristics of membrane structures, including statistics of displacement responses, oscillation frequency, and oscillation damping ratios, were identified from the perspective of time and frequency domains. Simultaneously, the particle image velocimetry system was employed to visualize the flow features, including velocity vector, turbulence intensity, and vortex evolution in both space and time. The flow modes were further decomposed by proper orthogonal decomposition (POD) to capture the salient aspects of the flow. Three patterns of POD modes are identified, and the first mode plays the dominant role in POD modes. It showed that as the wind Reynolds number increases, the space between the shear layer and membrane surface would be narrowed, and resultantly the vortices turn out smaller in scale and closer in space. This trend leads to an increase in the frequency of vortex shedding and a stronger FSI effect. When the frequency of vortex shedding approaches the fundamental frequency of structures, the vibration of the membrane would be shifted from turbulent buffeting to vortex-induced resonance, featured with lock-in frequency, significant amplified displacement, and negative aerodynamic damping ratio.

Fluid–acoustic–structure resonance mechanism of a plane cascade via a low-speed wind tunnel test

Acoustic resonance is an important factor that contributes to aeroengine compressor failure. In this study, a plane cascade of compressor blades was designed to reproduce acoustic resonance via a low-speed wind tunnel test. A high-frequency hot-wire, microphone and strain gauge were used to synchronously measure the fluid, acoustic and structural parameters. We analysed the variation in the amplitude and frequency of the multi-field parameters with increasing mean flow velocity and explored the multi-field interaction mechanism that induces the acoustic resonance of the plane cascade. The plane cascade effectively reproduced the acoustic resonance phenomenon. The first-order acoustic-mode frequency of the plane cascade flow duct, second-order torsional vibration mode frequency of the blade and shedding mode frequency of the tip clearance leakage vortex were equal under acoustic resonance. The fluid, acoustic and structural fields showed a strong interaction effect, achieving the maximum blade vibration amplitude and causing fatigue cracks of torsional vibration at the blade root. The frequency lock-in region of the compressor plane cascade was divided into an ‘acoustic–structure’ interaction region, a ‘fluid–acoustic–structure’ interaction region and a first-order acoustic-mode dominant region with increasing mean flow velocity, which demonstrates an interesting phenomenon in which the fluid–acoustic–structure modes compete: acoustic mode > blade vibration mode > vortex shedding mode. The results demonstrate a unique approach to the study of acoustic resonance that provides insight into the acoustic resonance mechanism in a cascade of compressor blades.

Ice-Induced Vibration Analysis of Fixed-Bottom Wind Turbine Towers

This research tackles the challenge of ice-induced vibrations in fixed-bottom offshore wind turbines, particularly the risk of frequency lock-in (FLI), a critical loading condition arising from slow ice movement against structures. We introduce an innovative FLI analysis process grounded in the ductile damage–collapse (DDC) mechanism, which offers a more accurate and significantly lower probability of FLI occurrence than conventional methods. Through dynamic evaluations employing a time-domain ice load model and FLI displacement analyses, we demonstrate that FLI can lead to higher structural vibrations than those caused by continuous brittle ice crushing. A case study of a 5 MW monopile wind turbine tower utilising Abaqus confirms the necessity for incorporating FLI considerations into structural design to ensure safety and performance in ice-prone environments. Comparing the DDC mechanism with the ISO method, our study reveals that the DDC approach predicts higher displacement and acceleration values during FLI, nearly an order of magnitude greater than those induced by ice loads with a 50-year return period. The research underscores the importance of robust ice-load integration in design strategies for offshore wind turbines, especially in regions susceptible to ice. It highlights the DDC mechanism as a novel strategy for enhancing structural resilience against ice-induced hazards.

Self-induced non-synchronous resonance phenomena and stability in reduced aero-elastic system

The paper is aimed at the parametric dynamic analysis of the two degrees of freedom (DoF) phenomenological model of aero-elastic interaction between a friction-damped flexible mounted body and a flowing fluid. A coupled system of a linear structure oscillator and the van der Pol based wake oscillator is introduced. Firstly, the complex eigenvalue problem is used for the comprehensive analysis of frequency lock-in, veering and crossing areas from the structural mode stability point of view. Further, an in-depth analysis of the fully nonlinear model based on the numerical continuation method is presented. The analysis focuses on non-synchronous vibration in the resonance areas. Attention is paid to the investigation of transition mechanisms to frequency lock-in and frequency veering in the structural response. In experimental studies, the amplitude and frequency jumps are observed. Here, we show that the origin of these jump phenomena results from the mutual coexistence of two stable solutions, which form a hysteresis region, which can be found in experimentally gained data. Moreover, the influence of structure friction-damping on nonlinear response is evaluated. The proposed phenomenological model is validated concerning two different experimental-based investigations.

Modeling and vortex-induced vibrations of semi-submersible floating offshore wind turbines

A rigid-flexible coupling dynamic model of a semi-submersible floating offshore wind turbine (FOWT) is established, and the characteristics of vortex-induced vibration (VIV) of the tower are studied. Lagrange’s equation is used to establish the equations of motion of a semi-submersible FOWT, a wake oscillator model is applied to simulate the interaction between tower and wind field, and the semi-empirical parameters in the wake oscillator model are optimized by computational fluid dynamics (CFD) method. The VIV characteristics of the semi-submersible FOWT before and after hoisting are investigated, and the influence of waves on VIV is analyzed. The results show that the VIV of tower bending mode with large amplitude of the semi-submersible FOWT will occur when the wind speed is in certain ranges, and the possibility of VIV of rigid-body modes with large amplitudes of the tower is low. The amplitudes of VIV and corresponding wind speed ranges can be greatly reduced, and the frequency lock-in domains will become narrower after hoisting the rotor system. The action of waves can reduce the amplitudes of VIV and cause the deviation of frequency lock-in domains, which may widen the coverage of wind speed of lock-in domains.

Experimental investigation into lock-in characteristics of the composite hydrofoils

Abstract This study experimentally investigates the lock-in characteristics of structural vibration of hydrofoils made of CFRP composite material. The synchronous experimental measurement system constituted of high-speed framing camera, LDV, velocity and pressure regulation systems are set up. It can be found that the Com+45° hydrofoil accelerates the cavitation inception, and the Com-45° hydrofoil defers it. The evolution of the dominant vibration frequency and cloud cavity shedding frequency are semblable. As the cavitation evolution gradually develops, the larger dominant frequency reduces, while the lower frequency remains unchanged. The scope of frequency lock-in meets the magnitude relationship Com+45° hydrofoil> Com-45° hydrofoil> Com0° hydrofoil. The wavelet transformation of structural vibration displacement and non-dimensional cavity area shows that both f shed and f shed,lock-in exist in the lock-in condition.

Experimental and Numerical Study of the Flow Around Rigid and Flexible Hydrofoils for Wetted and Cavitating Flow Conditions

Abstract The hydro-elastic response of a flexible NACA 0015 hydrofoil is investigated for both wetted and cavitating flow conditions. Computational fluid dynamics (CFD) analysis are performed using a fully implicit coupling between the ISIS-CFD solver (developed by the METHRIC team at Ecole Centrale de-Nantes) and a modal approach for the structure. The Reynolds-averaged Navier–Stokes (RANS) solver is first validated for wetted and cavitating flow conditions around a similar rigid hydrofoil, with experimental results carried out at the hydrodynamic tunnel of the French Naval Academy, including lift and drag measurements and high speed camera images. Then the numerical predictions for the flexible hydrofoil response are compared with experimental bending shapes and vibrations amplitudes, with a focus on cavitating flow conditions. For wetted flow conditions, numerical results show a good agreement with the experiments, for both rigid and flexible hydrofoils. For cavitating flow conditions, the hydro-elastic response is dominated by vibrations at the hydrofoil modal frequencies and the reentrant jet instability frequency. For the lowest values of the cavitation number, a large amplitude peak is experimentally observed in the frequency response spectra, due to lock-in between the first modal frequency and the reentrant jet frequency. Strong harmonics of this dominant peak also appear in the spectra, revealing a nonlinear response of the hydrofoil. While the amplitudes of vibrations are well predicted by the computations, the frequency lock-in observed in the experiments is not captured by the numerical model.

Shelving Spectroscopy and Atomic Clock Development of the Strontium 689 nm Intercombination Line

Abstract Precise timekeeping is crucial for a myriad of applications, including GPS, telecommunications, financial transaction time-stamping, and more [20]. The burgeoning demand for increasingly accurate clocks at a smaller scale has driven significant progress in atomic clock miniaturization over the past two decades [8][10]. Chip-scale atomic clocks have emerged by employing micro-fabricated vapor cells containing atomic species conducive to high-precision timekeeping [20][12]. Strontium has emerged as an exceptional candidate for atomic clocks, with the development of clocks exhibiting deviations of less than 1 second in 300 billion years [5]. However, a chip-scale strontium clock remains to be realized. This paper delineates the advancements made toward the development of a strontium atomic clock utilizing a micro-fabricated vapor cell. The proposed design involves implementing a shelving spectroscopy scheme that employs the 1S0-3P1 transition as the clock transition. Further refinement of the shelving scheme and the associated laser lock systems is necessary prior to the establishment of a functional clock. All components of this proposed design, encompassing both optical and electrical elements, can be miniaturized to chip scale, rendering it a promising solution for a wide range of applications with stringent weight and volume constraints. The strontium clock design outlined in this paper incorporates frequency and phase lock systems, which are critical for achieving precise resonance between the shelving and intermediate lasers with their respective transitions. This paper discusses the current limitations of these locking systems and proposes potential improvements. Once the frequency and phase locks are optimized and an additional frequency lock is employed, a clock is created by pairing a frequency counter with the laser resonant with the clock transition. Lay Summary I completed the work for this thesis under the supervision of Dr. Yang Li and Dr. Matthew Hummon at the Time and Frequency Division of the National Institute of Science and Technology. One of the aims of this research group is to produce increasingly precise and small clocks. High-precision timekeeping is essential to many sectors of the economy, from finance to telecommunications. However, a lot of new technology that requires the highest precision clocks does not have the space to accommodate the large atomic clocks of the past. The first atomic clocks occupied an entire laboratory. Today, the most precise atomic clocks can be as small as a dining room table. This research group hopes to make a clock that is the size of a computer chip. My thesis documents the progress I made in the pursuit of this goal. I primarily discuss the techniques used to measure and stabilize light. Light is essential for this atomic clock because it serves as the oscillator used to measure time, just like the pendulum for a grandfather clock. The name atomic clock comes from the use of atoms to stabilize the light. A group of atoms absorbs some of the light used for the clock. We then use a technique called shelving spectroscopy to amplify this absorption signal. This amplified absorption signal allows for better stabilization of the light through a technique called a phase lock. The phase lock prevents the frequency of the light from drifting too much, leading to a more reliable clock. My work contributes to the eventual development of a strontium-based atomic clock that is as small as a computer chip yet remains as precise as much larger clocks. Works Cited in Abstract [5] EurekAlert! Ultraprecise atomic clock poised for new physics discoveries, feb 2022.[8] S. Knappe, V. Gerginov, P. D.D. Schwindt, V. Shah, H. G. Robinson, L. Hollberg, and J. Kitching. Atomicvapor cells for chip-scale atomic clocks with improved long-term frequency stabil- ity. Opt. Lett., 30(18):2351–2353, Sep 2005.[10] Svenja Knappe, V Shah, Peter Schwindt, Leo Hollberg, John Kitching, Li-Anne Liew, and John Moreland.A microfabricated atomic clock. (85), 2004-01-01 2004.[12] Li-Anne Liew, Svenja Knappe, John Moreland, Hugh Robinson, Leo Hollberg, and John Kitching.Microfabricated alkali atom vapor cells. Appl. Phys. Lett., 84(14):2694–2696, April 2004.[20] Bonnie L Schmittberger and David R Scherer. A review of contemporary atomic frequency standards.2020. For the full text, please visit https://scholar.colorado.edu/concern/undergraduate_honors_theses/5712m8055.

Frequency lock-in control and mitigation of nonlinear vortex-induced vibrations of an airfoil structure using a conserved-mass linear vibration absorber

We investigate the effectiveness of a vibration absorber on the vortex-induced vibration response of turbine blades during the frequency lock-in phase. A reduced-order model of a turbine blade and van der Pol oscillator is used to represent the fluid–blade interaction caused by the vortex shedding. A spring-mass-damper system is considered to model the vibration absorber. The advantage of the vibration absorber is demonstrated by simulating the nonlinear coupled four-degree-of-freedom aeroelastic system for the different sets of system parameters. We observe the dominance of a nonlinear vibration absorber over the linear vibration absorber only for the higher coupling parameter values. The analytical solution of the nonlinear coupled system is obtained through the method of multiple scales for the case of 1:1 internal resonance to identify the critical design parameters of the vibration absorber. We observe the high sensitivity of the system's frequency response to the distance of the vibration absorber from the elastic axis, along with the absorber's damping, stiffness, and mass. Finally, we perform a parametric analysis on the lock-in of the stability region to better understand the effect of the vibration absorber on the instability region.

Numerical Analysis of Flow-Induced Transverse Vibration of a Cylinder with Cubic Non-Linear Stiffness at High Reynolds Numbers

Numerical calculations were performed to study the vortex-induced vibration (VIV) of a circular cylinder, which was elastically supported by springs of linear and cubic terms. These simulations were conducted at high Reynolds numbers ranging from 4200 to 42,000. To simulate the cylinder’s motion and the associated aerodynamic forces, Computational Fluid Dynamics were employed in conjunction with dynamic mesh capabilities. The numerical method was initially verified by testing it with various grid resolutions and time steps, and subsequently, it was validated using experimental data. The response of cubic nonlinearities was investigated using insights gained from a conventional linear vortex-induced vibration (VIV) system. This 2D study revealed that both the amplitude and frequency of vibrations are contingent on the flow velocity. The highest output was achieved within the frequency lock-in region, where internal resonance occurs. In the case of a hardening spring, the beating response was observed from the lower end of the initial branch to the upper end of the initial branch. The response displacement amplitude obtained for the linear spring case was 27 mm, whereas in the cubic nonlinear case, the value was 31.8 mm. More importantly, the results indicate that the inclusion of nonlinear springs can substantially extend the range of wind velocities in which significant energy extraction through vortex-induced vibration (VIV) is achievable.

Flow–acoustic resonance mechanism in tandem deep cavities coupled with acoustic eigenmodes in turbulent shear layers

This study presents the interplay of flow and acoustics within tandem deep cavities, focusing on the resonance mechanism occurring between turbulent shear layers and acoustic eigenmodes. The arrangement inside the tandem deep cavities includes both close and remote configurations. A combined fully coupled and decoupled aeroacoustic simulation strategy was devised. Employing an advanced high-order spectral/hp element method in conjunction with implicit large eddy simulation, the nonlinear compressible Navier–Stokes equations were solved to acquire internal flow–acoustic resonant field. In parallel, the linearized Navier–Stokes equations were tackled to determine coherent shear layer perturbations with external acoustic forcing. Based on acoustic measurements, the mainstream Reynolds number approaches approximately $R{e_{in}} = {O}({10^5})$ , where we identified the presence of frequency lock-in and a resonance range. Aeroacoustic noise sources were examined by implementing spectral proper orthogonal decomposition to decompose the pressure fields into hydrodynamic and acoustic components. As feedback intensified, the flow characteristics by the acoustic forcing effect and the flow-interactive effect were categorized according to the development of concurrent turbulent shear layers. Subsequently, the alternating and synchronous behaviours of concurrent shear layers resonated with the out-of-phase and in-phase acoustic eigenmodes were identified, and the corresponding large-scale counter-rotating vortex pairs and co-rotating vortex structures at the cavity entrances were extracted. The acoustic power generated by the Coriolis force was calculated using Howe's vortex-sound analogy, and the aeroacoustic energy transfer mechanism between large-scale shear layer vortices with acoustic eigenmodes was further explored. Finally, a linear response of coherent perturbations of the concurrent shear layers by external acoustic forcing was established. The amplification of flow in the streamwise direction toward the main duct led to the formation of coherent vortex structures, accompanied by separation bubbles into the main duct.

Replicating Spectral Baseline for Unambiguous Frequency Locking in Resonant Sensors.

Electrothermal piezoresistive resonant cantilever sensors have been fabricated with embedded actuating (heating resistor) and sensing (piezo resistors) parts, with the latter configured in a Wheatstone bridge circuit. Due to the close spacing between these two elements, a direct thermal parasitic effect on the resonant sensor during the actuating-sensing process leads to asymmetric amplitude and reversing phase spectral responses. Such a condition affects the precise determination of the cantilever's resonant frequency, f0. Moreover, in the context of phase-locked loop-based (PLL) resonance tracking, a reversing phase spectral response hinders the resonance locking due to its ambiguity. In this work, a replica of the baseline spectral was applied to remove the thermal parasitic effect on the resonance spectra of the cantilever sensor, and its capability was simulated through mathematical analysis. This replica spectral was subtracted from the parasitized spectral using a particular calculation, resulting in optimized spectral responses. An assessment using cigarette smoke particles performed a desired spectral shifting into symmetrical amplitude shapes and monotonic phase transitions, subsequently allowing for real-time PLL-based frequency tracking.

Optimal external forces of the lock-in phenomena for flow past an inclined plate in uniform flow.

We theoretically studied the optimal control, frequency lock-in, and phase lock-in phenomena due to the spatially localized periodic forcing in flow past an inclined plate. Although frequency lock-in is evident in many fluid phenomena, especially fluid-structure interactions, not many researchers have investigated it using a theoretical approach based on flow details. We obtained detailed information on the lock-in phenomena to external periodic forcing using phase reduction theory, a mathematical method for extracting the dynamics near the limit cycle. Furthermore, the optimal forces applied to the velocity field were determined under the condition of the minimum forcing energy and maximum lock-in range. The study of uniform periodic forces applied within spatially confined regions led to the conclusion that the effective lock-in position, which includes both the upstream and downstream areas of the plate, depends on the principal frequency of the force. The frequency lock-in range of these forces was analyzed and compared with theoretical predictions.

Elimination of lock-in phenomenon in vortex-induced vibration by passive modal control

Theoretical analysis and numerical results have shown that frequency lock-in in vortex-induced vibration (VIV) is caused by the instability of the structural mode rather than a resonant response to external excitations. However, there is a lack of experimental evidence supporting relevant theoretical research findings. This study investigates VIV suppression with a passive modal controller (PMC) for a circular cylinder at Reynolds numbers $Re = 60$ and $Re = 40$ , using experiments to distinguish the effects of stable and unstable wake modes. Comparative analysis before and after the implementation of the PMC reveals significant reduction in the vibration amplitude and the disappearance of the lock-in phenomenon at $Re = 60$ . The vibration frequency closely follows the vortex shedding frequency after control, while dynamic mode decomposition of the flow field indicates that the wake mode is dominant. For $Re = 40$ , the vibration is eliminated and the flow becomes steady. Additionally, the root loci of the coupled system are investigated before and after the PMC implementation via linear stability analysis. The results indicate that the PMC can alter the dynamic characteristics of the original system, causing the structural mode and PMC mode to couple when approaching the PMC frequency. Then, the interaction typically improves the stability of the structural mode. Finally, a parametric study is conducted in the experiment, as well as a linear stability analysis. The study provides experimental evidence that stability control of the structural mode is the key to suppressing VIV and eliminating the lock-in phenomenon.

Experimental and numerical investigations on non-synchronous vibration and frequency lock-in of transonic compressor rotor blades

Non-synchronous vibration (NSV) problems in axial compressors are challenging and frequently result in high vibration stress or structural failure within the frequency lock-in region. A deeper understanding of the lock-in phenomenon in NSV is necessary to improve blade reliability and safety. In this study, an experiment was conducted on a multistage transonic axial compressor to obtain frequency lock-in characteristics. The enforced motion of the flexible blade simulation method was used to study the frequency lock-in mechanism between blade vibration and tip unstable flow. The results showed that the aerodynamic frequency characteristic changed from a broadband spectrum to a distinct frequency peak as the NSV onset. The nonlinear vibration pattern could maintain the limited cycle oscillation for 26 s. The vibration stress of the frequency locked-in case was approximately 19 times that of the frequency unlocked one. The pressure fluctuations generated by the large-scale radial separation vortex structures were stronger than those of the tip leakage flow, and the third-order harmonic frequency of the circumferential instability flow was close to the first-order bending model natural frequency. The periodic shedding and reattachment process of flow separation provided the initial non-synchronous aerodynamic excitation source. The frequency lock-in phenomenon occurred at a maximum vibration amplitude of 2 % and 3 % tip chord length. The tip unstable flow characteristics were consistent and entirely dominated by blade vibration.

Coexistence of passive vortex-induced vibrations and active pitch oscillation triggered by a square cylinder attached with a deformable splitter plate

To understand passive vortex-induced vibrations (VIV) coexisting with active structure motions, this paper numerically investigates the use of pure pitch oscillation to control a square cylinder mounted with a deformable splitter plate at the Reynolds number of 333. The oscillation is enforced with an amplitude of 3° and different frequencies from 0 to 6 Hz. Direct numerical simulations using a partitioned method with a semi-implicit coupling algorithm are performed. According to the trajectories of the splitter-plate tip displacement with respect to the lift or drag force coefficient, a specific lock-in regime determined by the frequency of the enforced pitch oscillation is identified. Further spectral analyses of the tip displacement and lift force show that the lock-in frequencies are equal to the enforced frequencies. Next to the lock-in regime, semi-lock-in regimes with narrow bandwidths are distinguished, exhibiting both lock-in and non-lock-in features. In the non-lock-in regimes, the frequencies of the most predominant peaks in the spectra are found near the natural frequency of the splitter plate of 3.236 Hz, and the frequencies of the two secondary peaks are distributed along the characteristic lines following the ratios of these frequencies to the enforced frequency, which are ±1. Thus, the interaction is dependent on the combined effects of the passive VIV and the actively enforced pitch oscillations. Moreover, the intersection points of the characteristic lines are located close to the upper and lower frequency limits of the lock-in regime, inferring the conditions for the lock-in onset.

A deep learning approach to classifying flow-induced vibration response regimes of an elliptical cylinder

This study proposes a new approach that leverages deep learning to the study of flow-induced vibration (FIV), specifically to automate flow regime classification and to visualize the transitions between these regimes. Using previously obtained data on the amplitude response of an elastically mounted cylinder as a function of reduced velocity for a range of structural damping ratios, the time trace of the body displacement and fluid driving forces are first converted into a frequency-time representation using continuous wavelet transforms before being input to several pre-trained convolutional neural networks for feature extraction. When utilizing the outputs of each convolutional neural network for regime classification, we found that almost all the machine learning approaches had high cross-validation accuracy that was statistically insignificant from each other. The five best-performing classifiers were then used as an ensemble method, yielding a weighted accuracy of 99.1% on the test data. The FIV response regimes were further investigated by projecting the outputs of the pre-trained convolutional neural networks onto the first three modes identified with principal component analysis (PCA). The PCA plots indicated that, among all the models considered, Xception showed superior capability in delineating distinct locations for different FIV response regimes, based on the lock-in frequency and the presence of harmonics in the driving fluid forces. Moreover, the PCA plots also showed that increasing the structural damping ratio resulted in a diminished disparity in the dynamics of the identified FIV response regimes, leading to a less discernible separation between the regimes in the plots.

A frequency meter based on Costas FLL for resonant accelerometers

The resonant accelerometer (RA) is an important part for high-performance inertial devices. And high accuracy frequency measurement is one of the key technology for RA. This paper developed a frequency meter based on Costas frequency lock loop (FLL). This structure is flexible as the analog input sinusodial voltage wave is converted into digital domain by an ADC and the frequency measurement function dealing with that voltage could be implemented only with digital circuits. The transfer function of the frequency meter is determined by the loop filter of the FLL and the closed system is always stable for PID controller. The noise in the loop is reshaped by a first order ∑-Δ modulator formed by the frequency meter loop, which relaxes the requirement for the accuracy of ADC. A test board for the frequency meter is implemented with a 24-bit ADC and FPGA, and achieves a noise of 1mHz/Hz at low frequency band, 7µHz/Hz around 50 Hz with a 40 kHz sinusodial input voltage.