Amplitude Modulation Function Research Articles

Mechanisms of Reappeared Period Shifts of Internal Solitary Waves Based on Mooring Array Observations in the Northern South China Sea

AbstractMooring observations have revealed that the daily reappeared time (DRt) of internal solitary waves (ISWs) in the northern South China Sea (SCS) manifests systematic shifts. This study aims to reveal the dynamic mechanisms behind this phenomenon using the theory of modulation of shear flow to the internal tide wave (IT) propagation. Approximate solutions for the frequency modulation function (FMF) and the amplitude modulation function (AMF) of ITs are derived and validated by the mooring array measurements on the northern SCS continental shelf in 2019 and 2020. Namely, the mechanisms of the ISW reappeared period shift (RPS derived from DRt) and amplitude variation are attributed to the modulation of low‐frequency flow with a period of about 7 days to ITs. The FMF is induced by the vorticity of the low‐frequency flow (FS1) and the Doppler shift (FS2). Thus, the sign of the FMF value may be positive (blue shift) and negative (red shift), depending on the algebraic summation of the two terms. The FS2 derived from mooring observed velocities confirms the modulation effects of mean current on the frequency shift and the amplitude variation of ITs and ISWs.

Multi-shaker time-varying root mean square non-stationary random vibration environmental control test

The current multi-shaker random control methods concentrate on the simulation of stationary vibrations. This work presents an innovative technique for multi-shaker non-stationary random vibration environmental control test. Firstly, an amplitude modulation method is introduced to generate multi-input non-stationary random signals with time-varying root mean square values, whose kurtoses and moving RMS values are specified by amplitude modulation functions. Then, the generated signals are applied as excitation signals for the non-stationary random vibration environmental control test. The response signals of a linear vibration system under non-stationary excitations are derived in the frequency domain. The derived formulas for kurtoses and moving RMS values are also applicable to non-stationary response signals. Meanwhile, the stationary power spectral densities of response signals are put forward. When the amplitude modulation functions are zero mean Gaussian distributions, the power spectral densities of the response signals can be directly calculated. Ultimately, the control of kurtoses, moving RMS values and stationary power spectral densities of response non-stationary random signals is realized. Simulation and experimental examples both adopt a two-input two-output beam vibration system and the results prove the correctness and practicability of the proposed method. The presented control procedure is concise and efficient in simulating multi-shaker non-stationary random vibration environments.

HTG transformation: an amplitude modulation method and its application in bearing fault diagnosis

Abstract Rolling bearings are critical components in modern mechanical equipment, and the health monitoring and predictive maintenance of bearings are crucial for the normal operation of machinery. Hence, there is a compelling need to delve into advanced methodologies for enhancing the detection of fault characteristics in bearings. Faulty bearings produce periodic impulses during constant-speed rotation, which can typically be detected through envelope analysis. However, in some complex conditions, the relevant fault frequencies may be hidden within interfering components. This paper presents an amplitude modulation technique called the hyperbolic tangent Gaussian (HTG) transformation, designed to extract weak fault components from signals. Firstly, a family of amplitude modulation functions, known as the HTG functions, is constructed. These functions modulate signals with normalized amplitudes to obtain a series of modulated signals. Simultaneously, a frequency domain amplitude ratio metric is used for the automatic selection of the optimal components. Finally, the HTGgram is introduced, a spectral decomposition method based on trend components, aiming to identify the best combination of filtering and modulation components. Simulations with multi-component bearing fault signals and experimental signals with composite bearing faults demonstrate that this method not only highlights fault features and suppresses noise interference but also adaptively selects frequency bands related to faults, enhancing fault information. This approach exhibits excellent adaptability and effectiveness in complex operating conditions with multiple interference components.

Modified time domain randomization technique for multi-shaker non-stationary non-Gaussian random vibration control

Traditional random vibration environmental tests simulate stationary Gaussian random vibration environments. In this work, the generation and closed-loop control of multi-shaker non-stationary non-Gaussian random vibration signals with the modified time domain randomization technique are studied. The amplitude modulation function is introduced to control the non-stationary and non-Gaussian characteristics that the root mean square value of the generated signal changes with time. The kurtosis relationship between the one frame pseudo-random signal and consecutive true random signal is derived theoretically. It is found that the kurtosis of the consecutive non-stationary random signal is determined by the amplitude modulation function and kurtosis of the pseudo-random signal. The standard deviation of the time-varying root mean square reflects the non-stationary characteristics of the generated signal. A control strategy for multi-shaker non-stationary non-Gaussian random vibration environmental test is proposed. The non-stationary and non-Gaussian characteristics are extracted from the measured response signals so that the power spectral densities, kurtoses and non-stationary characteristics can be controlled simultaneously. The results from the simulation examples and multi-shaker vibration experiments prove the feasibility and practicability of the proposed non-stationary non-Gaussian random signal generation method and control strategy.

Random vibration environmental test based on strain response control

This paper presents a novel mechanical environmental test method that multi-output random strain responses are replicated instead of acceleration responses. In this work, the positive-definite strain reference spectral matrix and reference kurtoses for multiple control channels are defined first, and then three types of strain random signals including stationary Gaussian, stationary non-Gaussian, and non-stationary are generated. The inverse Fourier transform is used to obtain the stationary Gaussian strain random signals and the stationary non-Gaussian strain signals are obtained by the zero-memory nonlinear transformation. To synthetize non-stationary strain random signals, an amplitude modulation function is introduced with time-varying root mean square values. The correction algorithms are employed to update the drive signals for matching the strain responses compared with corresponding reference values. The simulation and experimental results prove the effectiveness and feasibility of the proposed strain response control procedure. The presented work provides new perspectives to investigate the fatigue behavior and life estimation of structure under controlled strain response environments for vibration fatigue tests.

Modeling response spectrum compatible pulse-like ground motion

The seismic response analysis of near-fault pulse-like ground motions is severely restricted due to the scarcity of pulse-like records. The requirement in regulations that the response spectra of artificial ground motions should be compatible with the target response spectrum makes the relevant studies more difficult. As a result, this study proposes a trigonometric series-based stochastic method to simulate pulse-like ground motions, with the advantage that the corresponding pseudo-spectral acceleration is compatible with the given target response spectrum. This goal is achieved by two parts. (1) The envelope function of pulse-like records obtained by the Hilbert transform is utilized as the amplitude modulation function to ensure that the simulated ground motion contains a pulse. (2) A novel iteration scheme based on random frequency parameters is proposed to guarantee the response spectrum compatibility. The velocity ground motion is first simulated since the pulse usually exists in velocity. The ground-motion acceleration subsequently obtained by differentiating the velocity is adopted to calculate the response spectrum. Two cases are implemented and verified the effectiveness of the proposed method in enriching existing pulse-like databases and generating pulse-like ground motion in areas that lack records. Moreover, the amplitude modulation function and target spectrum, as two key factors in the proposed method, determines the presence of a pulse and the pulse periods, respectively. This property makes the proposed method potentially universal applicability for stochastic pulse-like ground motion simulation in engineering.

Nonlinear dynamics of a spur gear pair with tooth root crack based on an amplitude modulation function

PurposeGear transmissions are widely utilized in practice. This paper aims to uncouple the crack feature from the cracked time-varying mesh stiffness (TVMS) and investigate the effects of the crack on the nonlinear dynamics of a spur gear pair.Design/methodology/approachAn approximate method to simulate the cracked TVMS is proposed by using an amplitude modulation function. The ratio of mesh stiffness loss is introduced to estimate the TVMS with different crack depths and angles. The dynamic responses are obtained by solving a torsional model which takes the non-loaded static transmission error, the backlash and the cracked TVMS into account. By using the bifurcation diagram, the largest Lyapunov exponent (LLE) and dynamic mesh force, the influences of crack on nonlinear behaviors are examined. The dynamic characteristics are identified from the phase diagram, Poincaré map, dynamic mesh force, time series and FFT spectra.FindingsThe comparison between the healthy and cracked gear pairs indicates that the crack affects the system motions, such as the obvious changes of impact force and unpredictable instability. Besides, the additive and difference combination frequencies can be found in periodic-1 and -2 motions, but they are covered in periodic-3 and chaotic motions. Deeper crack is an important determinant of the nonlinear behaviors at a higher speed.Originality/valueThe research provides an interesting perspective on cracked TVMS and reveals the connection between crack and nonlinear behaviors of the gear pairs.

A Bridge-Type Inductance Sensor With a Two-Stage Filter Circuit for High-Precision Detection of Metal Debris in the Oil

A bridge-type inductance sensor with a two-stage filter circuit for high-precision detection of metal debris in the oil is proposed. The sensor mainly consists of a bridge-structure sensing unit and a two-stage filter circuit. The sensing unit consists of two double-wire solenoid coils (as the detection unit and the reference unit, respectively) and a Wheatstone bridge -structure. This structure enhances the response of the detection unit to the magnetic field disturbance generated by the wear debris and can improve the detection accuracy of the sensor. Furthermore, a circuit with rectification, amplitude modulation, and amplification functions is introduced to eliminate the noise interference from the environment and the system, and to accurately extract the weak abrasive signals that are submerged in the noise. Meanwhile, by adjusting the passband gain of the two-stage filter circuit, the measurement range of the sensor voltage value is improved. Experimental results show that adding a two-stage filter circuit can improve the resolution of the sensor, and can effectively detect <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$45~\mu \text{m}$ </tex-math></inline-formula> iron particles. The sensor provides technical support for the modularity and portability of the testing instrument, which is essential for fault diagnosis and prevention of the hydraulic systems.

Configurational complexity of nonautonomous discrete one-soliton and rogue waves in Ablowitz-Ladik-Hirota waveguide

We compute the configurational complexity (CC) for discrete soliton and rogue waves traveling along an Ablowitz-Ladik-Hirota (ALH) waveguide and modeled by a discrete nonlinear Schrödinger equation. We show that for a specific range of the soliton transverse direction κ propagating along the parametric time ζ(t), CC reaches an evolving series of global minima. These minima represent maximum compressibility of information in the momentum modes along the Ablowitz-Ladik-Hirota waveguide. Computing the CC for rogue waves as a function of background amplitude modulation μ, we show that it displays two essential features: a maximum representing the optimal value for the rogue wave inception (the “gradient catastrophe”) and saturation representing the rogue wave dispersion into constituent wave modes. We show that saturation is achieved earlier for higher values of modulation amplitude as the discrete rogue wave evolves along time ζ(t).

Acoustic energy transport characteristics based on amplitude and phase modulation using waveguide array

To realize the multi-functional manipulation of the acoustic field with a simple artificial structure, a waveguide array based on resonant units was proposed in this work. Based on the transmission spectrum and zero-like refractive index of the waveguide unit, the amplitude of the transmitted wave can be manipulated. By changing the size of the waveguide unit flexibly, the phase of the transmitted wave can be manipulated. In addition, by extending the waveguide array to the sub-wavelength scale, an acoustic metasurface with both amplitude and phase modulation functions can be implemented, which provides new ways for the design of lightweight artificial periodic structures.

On the Estimation of Power Spectral Density and Lagged Coherence of Time Transformed Nonstationary Seismic Ground Motions and Their Use to Simulate Synthetic Records

ABSTRACT Ground motions could be modelled as amplitude and frequency modulated process. The frequency modulation through a time transformation results in the modelled motions in the new timescale being a stationary process except for the amplitude modulation. The assessment of power spectral density (PSD) and the lagged coherence in the transformed timescale is presented in this study. It is shown theoretically and numerically that the PSD functions obtained through time transformation in the original timescale should not be used as an amplitude modulation function, and that the lagged coherence in the new or auxiliary timescale differs from that in the original timescale.

A novel coordinated detection method for transmissive/reflective sensors against strong in-band interference

Accuracy of transmissive/reflective sensors is usually degraded by strong in-band interference, especially those with frequencies very close or even equal to that of the measured signal. To tackle this challenge, this paper proposes a novel detection method including three units: a coordinated modulator (CM), a high-performance analog narrow-band filter (ANBF), and a smart digital filtering algorithm (SDFA). The CM performs a mixed function of amplitude modulation and phase modulation, and is used to control the sensor’s transmitter to circularly transmit the signal modulated according to the coordinated time-sequence requirement from the SDFA. The ANBF has a very narrow passband to make the analog signal sampled by the SDFA only include the measured signal and an in-band interfering component. The SDFA utilizes the properties of odd/even functions and the definitions of power in A.C. circuit to filter out the in-band interfering component, with the coordination of the CM and ANBF. Effectiveness of the proposed method is validated via simulations and laboratory tests setting up based on a real application case of electromagnetic mold level detection under mold-electromagnetic stirring operating condition. Test results show that the proposed method can effectively deal with strong in-band interfering signal with the frequency very close or even equal to that of the measured signal. In the total of 20000 simulation cases, attenuations of in-band interference can exceed −76 dB. Moreover, in the experimental tests under a condition of −40 dB signal-to-noise ratio, measurement errors of the amplitude of the measured signal can be achieved less than 1.88%.

Pulse doublets generated by a frequency-shifting loop containing an electro-optic amplitude modulator.

We investigate theoretically and experimentally an all-fibered frequency-shifting loop which includes an electro-optic amplitude modulator (EOM) and an optical amplifier, and is seeded by a continuous-wave laser. At variance with frequency-shifted feedback lasers, or Talbot lasers, that contain an acousto-optic frequency shifter, the EOM creates at each round-trip two side-bands that recirculate inside the loop. Benefiting from the high modulation frequency of the EOM, a wide optical frequency comb up to 40 GHz is generated. We demonstrate an original double-pulse regime when the loop length is a multiple of the RF modulation wavelength applied to the modulator. The inter-pulse interval is governed by both the bias voltage and modulation depth of the EOM. Besides, some typical waveforms such as saw-tooth and rectangle are experimentally obtained by properly setting operating frequency, bias voltage and the RF power. The system is modeled by a linear interference model that takes the amplitude modulation function and loop delay into account. The model explains the formation of pulse doublets and reproduces well all the experimental waveforms. Furthermore, the un-seeded loop driven above threshold also generates mode-locked picosecond pulse doublets with a continuously adjustable delay up to the modulation period.

Enhanced Damping Estimation for Cable-Stayed Bridges Based on Operational Monitoring Data

This study proposes an enhanced damping estimation procedure for flexible cable-supported bridges based on operational modal analysis (OMA). The OMA approach combines the natural excitation technique (NExT) with an eigensystem realization algorithm (ERA). An amplitude modulating (AM) function is introduced to stationarize the vehicle-induced responses. This study proposes guidelines for the selection of parameters for the NExT–ERA algorithm and AM-based stationarization. The proposed damping estimation procedure and parameter selection guidelines were applied to the data gathered from measuring an in-service cable-stayed bridge over a three-day period. The correlations between the identified damping ratios and environmental factors such as vibration level, temperature and wind velocity were investigated. The effect of aerodynamic damping during OMA is also discussed. The examined data identifies the amplitude-dependency of the damping ratios.

Electrically-driven pure amplitude and frequency modulation in a quantum cascade laser

We present pure amplitude modulation (AM) and frequency modulation (FM) achieved electrically in a quantum cascade laser (QCL) equipped with an integrated resistive heater (IH). The QCL output power scales linearly with the current applied to the active region (AR), but decreases with the IH current, while the emission frequency decreases with both currents. Hence, a simultaneous modulation applied to the current of the AR and IH sections with a proper relative amplitude and phase can suppress the AM, resulting in a pure FM, or vice-versa. The adequate modulation parameters depend on the applied modulation frequency. Therefore, they were first determined from the individual measurements of the AM and FM transfer functions obtained for a modulation applied to the current of the AR or IH section, respectively. By optimizing the parameters of the two modulations, we demonstrate a reduction of the spurious AM or FM by almost two orders of magnitude at characteristic frequencies of 1 and 10 kHz compared to the use of the AR current only.

Damping Identification of Bridges Under Nonstationary Ambient Vibration

This research focuses on identifying the damping ratio of bridges using nonstationary ambient vibration data. The damping ratios of bridges in service have generally been identified using operational modal analysis (OMA) based on a stationary white noise assumption for input signals. However, most bridges are generally subjected to nonstationary excitations while in service, and this violation of the basic assumption can lead to uncertainties in damping identification. To deal with nonstationarity, an amplitude-modulating function was calculated from measured responses to eliminate global trends caused by nonstationary input. A natural excitation technique (NExT)-eigensystem realization algorithm (ERA) was applied to estimate the damping ratio for a stationarized process. To improve the accuracy of OMA-based damping estimates, a comparative analysis was performed between an extracted stationary process and nonstationary data to assess the effect of eliminating nonstationarity. The mean value and standard deviation of the damping ratio for the first vertical mode decreased after signal stationarization.

Two-state model of a general Heun class with periodic level-crossings

We present a specific constant-amplitude periodic level-crossing model of the semi-classical quantum time-dependent two-state problem that belongs to a general Heun class of field configurations. The exact analytic solution for the probability amplitude, generally written for this class in terms of the general Heun functions, in this specific case admits series expansion in terms of the incomplete Beta functions. Terminating this series results in an infinite hierarchy of finite-sum closed-form solutions each standing for a particular two-state model, which generally is only conditionally integrable in the sense that for these field configurations the amplitude and phase modulation functions are not varied independently. However, there exists at least one exception when the model is unconditionally integrable, that is the Rabi frequency and the detuning of the driving optical field are controlled independently. This is a constant-amplitude periodic level-crossing model, for which the detuning in a limit becomes a Dirac delta-comb configuration with variable frequency of the level-crossings. We derive the exact solution for this model, determine the Floquet exponents and study the population dynamics in the system for various regions of the input parameters.

Computer-based model for the transient dynamics of a tall building during digitally simulated Andrews AFB thunderstorm

Thunderstorm downbursts are near ground-level meteorological hazards, exhibiting transient, non-synoptic, short-duration and high intensity wind velocities. Winds can induce nonstationary loads and large-amplitude dynamic response in a slender vertical structure. The thunderstorm-induced response against non-synoptic wind loads is extremely complex and cannot be investigated by conventional wind analysis approaches. This study examines the thunderstorm-induced dynamic response of tall buildings. The wind load is based on the observation of the Andrews Air Force Base (AFB) thunderstorm. The main objectives are to: (i) reconstruct the Andrews thunderstorm wind speed record and replicate structure, lifecycle and the fundamental wind parameters, (ii) digitally synthesize the non-turbulent and turbulent velocities to derive aerodynamic loads on a reference tall building, (iii) formulate the thunderstorm-induced dynamics of the tall building subjected to the Andrews thunderstorm-induced downburst loads, and (iv) investigate the response of a tall building by considering two different plausible scenarios. Some unanswered scientific questions are investigated: uncertainty in vertical wind velocity profiles, abrupt change of wind direction angles and influence of crosswind velocities. Three amplitude modulation functions are employed to simulate the transient turbulent field observed during the Andrews thunderstorm. Numerical simulations analyze the dynamic response of the 183-m CAARC tall building.

Automatic characteristic frequency association and all-sideband demodulation for the detection of a bearing fault

This paper proposes advanced signal-processing techniques to improve condition monitoring of operating machines. The proposed methods use the results of a blind spectrum interpretation that includes harmonic and sideband series detection. The first contribution of this study is an algorithm for automatic association of harmonic and sideband series to characteristic fault frequencies according to a kinematic configuration. The approach proposed has the advantage of taking into account a possible slip of the rolling-element bearings. In the second part, we propose a full-band demodulation process from all sidebands that are relevant to the spectral estimation. To do so, a multi-rate filtering process in an iterative schema provides satisfying precision and stability over the targeted demodulation band, even for unsymmetrical and extremely narrow bands. After synchronous averaging, the filtered signal is demodulated for calculation of the amplitude and frequency modulation functions, and then any features that indicate faults. Finally, the proposed algorithms are validated on vibration signals measured on a test rig that was designed as part of the European Innovation Project ‘KAStrion’. This rig simulates a wind turbine drive train at a smaller scale. The data show the robustness of the method for localizing and extracting a fault on the main bearing. The evolution of the proposed features is a good indicator of the fault severity.

Ambient modal identification using non-stationary correlation technique

The topic of this paper is the modal identification from non-stationary ambient response data by applying correlation technique. It is shown theoretically that by assuming the ambient excitation to be non-stationary white noise in the form of a product model, the non-stationary response signals can be converted into free vibration data via the correlation technique. Previous studies have showed that the practical problem of insufficient data samples available for evaluating non-stationary correlation can be approximately resolved by first extracting the amplitude-modulating function from the response and then transforming the non-stationary responses into stationary ones. However, the errors involved in the approximate free-decay response would generally lead to a distortion in the modal identification. In the present paper, we propose that, if the ambient excitation can be represented by a product model with slowly time-varying function, without any additional treatment of transforming the original nonstationary responses, the non-stationary responses of the system can be treated approximately as a stationary random process; then, the nonstationary cross correlation functions of structural response evaluated at an arbitrary, fixed time instants of structural response are of the same mathematical form as that of free vibration of a structure, from which modal parameters of the original system can thus be identified. Numerical simulations, including one example of using the practical earthquake data served as the excitation input acting on a linear two-dimensional model of one-half of a railway vehicle, confirm the validity of the proposed method for identification of modal parameters from non-stationary ambient response data only.