Exploration of instantaneous frequency for local control assessment in real-time hybrid simulation

Local control parameters such as instantaneous delay and instantaneous amplitude play an essential role in evaluating the performance and maintaining the stability of real-time hybrid simulation(RTHS).However,existing methods have limitations in obtaining this local assessment in either the time domain or frequency domain.In this study,the instantaneous frequency is introduced to determine local control parameters for actuator tracking assessment in a real-time hybrid simulation.Instantaneous properties,including amplitude,delay,frequency and phase,are then calculated based on analytic signals translated from actuator tracking signals through the Hilbert transform.Potential issues are discussed and solutions are proposed for calculation of local control parameters.Numerical simulations are first conducted for sinusoidal and chirp signals with time varying amplitude error and delay to demonstrate the potential of the proposed method.Laboratory tests also are conducted for a predefined random signal as well as the RTHS of a single degree of freedom structure with a self-centering viscous damper to experimentally verify the effectiveness of the proposed use of the instantaneous frequency.Results from the ensuing analysis clearly demonstrate that the instantaneous frequency provides great potential for local control assessment,and the proposed method enables local tracking parameters with good accuracy.

High Sensitivity Digital Instantaneous Frequency Measurement Receiver for Precise Frequency Analysis

There are numerous applications, such as Radar, that leverage wideband technology. However, the presence of noise introduces certain limitations and challenges. It is crucial to harness wideband technology for applications demanding the rapid and precise transmission of diverse information from one point to another within a short timeframe. The ability to report a signal without tuning within the input bandwidth stands out as one of the advantages of employing a digital wideband receiver. As indicated, a digital wideband receiver plays a pivotal role in achieving high precision and accuracy. The primary distinction between Analog and Digital Instantaneous Frequency Measurement lies in the fact that analog Instantaneous Frequency Measurement (IFM) receivers have traditionally covered extensive input bandwidths, reporting one accurate frequency per short pulse. In the contemporary landscape, digital IFM systems utilize high-sampling-rate Analog-to-Digital Converters (ADC) along with Hilbert transforms to generate two output channels featuring a 90-degree phase shift. This paper explores the improvement of sensitivity in current digital IFM receivers. The optimization efforts target the Hilbert transform and autocorrelations architectures, aiming to refine the system’s ability to report fine frequencies within a noisy wide bandwidth environment, thereby elevating its overall sensitivity.

DEVELOPMENT OF VIRTUAL INSTRUMENT IN CHARACTERISTIC ANALYSIS OF ROTATING MACHINERY BASED ON INSTANTANEOUS FREQUENCY ESTIMATION

Based on the recently quick-developing time-frequency analysis (TFA)technique and virtual instrument (VI) technique, a virtual instrument in characteristic analysis ofrotating machinery is researched and developed successfully. By utilizing instantaneous frequencyestimation (IFE) theoretics of TFA technique, and based on IFE of peak searching on thetime-frequency spectrum, order analysis (OA) functions is put forward and implemented, such as orderspectrum, order spectrum matrix, order tracking, order tracking filtering, and order componentextraction, etc. Unlike the home and abroad existing popular characteristic analyzers, which needkey phasing devices such as shaft encoder, phase-locked loop (PLL), phase-locked multiple frequency,tachometer, etc, to implement constant angle sampling directly or indirectly, whereas thisinstrument only uses the vibration signal of rotating machinery to carry out OA. This instrumentmakes up the shortage of these traditional instruments in analyzing the non-stationary signal ofrun-up and run-down process of rotating machinery. Therefore, it is a great breakthrough for theexisting order analyzers.

Instantaneous frequency and wave mode identification in a magnetosheath using few spatial points

Observational data such as those obtained from the magnetosheath in the downstream of Earth＇s bow shock have waveforms that differ from those of sinusoidal signals. In practice, they are not even aggregates of sinusoidal signals. Therefore, the frequency decomposition for the data requires technique that will account for the time-varying features of the data that will lead to deduction of physical meaning of the observations. The combination of empirical mode decompo- sition （EMD） and Hilbert transform has been used for extracting the various contributing oscillatory modes （EMDs） and the instantaneous frequency determination （Hilbert transform） of every physically meaningful mode called intrinsic mode func- tion （IMF）. The resulting instantaneous frequencies are used to determine instantaneous wave vectors. The combination of the instantaneous frequencies and wave vectors is useful in the identification of wave modes based on the characteristics of the waves. The results show that EMD-Hilbert can be more reliable than simple Hilbert transform alone.

Instantaneous frequency measurement using two parallel I/Q modulators based on optical power monitoring

A scheme for instantaneous frequency measurement(IFM)using two parallel I/Q modulators based on optical power monitoring is proposed.The amplitude comparison function(ACF)can be constructed to establish the relationship between the frequency of radio frequency(RF)signal and the power ratio of two optical signals output by two I/Q modulators.The frequency of RF signal can be derived by measuring the optical power of the optical signals output by two I/Q modulators.The measurement range and measurement error can be adjusted by controlling the delay amount of the electrical delay line.The feasibility of the scheme is verified,and the corresponding measurement range and measurement error of the system under different delay amounts of the electrical delay line are given.Compared with previous IFM schemes,the structure of this scheme is simple.Polarization devices,a photodetector and an electrical power meter are not used,which reduces the impact of the environmental disturbance on the system and the cost of the system.In simulation,the measurement range can reach 0 GHz-24.5 GHz by adjusting the delay amount of the electrical delay lineτ=20 ps.The measurement error of the scheme is better at low frequency,and the measurement error of low frequency 0 GHz-9.6 GHz can reach-0.1 GHz to+0.05 GHz.

IMPROVED METHOD FOR HILBERT INSTANTANEOUS FREQUENCY ESTIMATION

In the mechanical fault detection and diagnosis field, it is more and more important to analyze the instantaneous frequency （IF） character of complex vibration signal. The improved IF estimation method is put forward aiming at the shortage of traditional Hilbert transform. It is based on Hilbert transform in wavelet domain. With the help of relationship between the real part and the imaginary part obtained from the complex coefficient of continuous wavelet transform or the analyti- cal signal reconstructed in wavelet packet decomposition, the instantaneous phase function of the subcomponent is extracted. In order to improve the precise of IF estimated out, some means such as Linear regression, adaptive filtering, resampling are applied into the instantaneous phase obtained, then, the central differencing operator is used to get desired IF. Simulation results with synthetic and gearbox fault signals are included to illustrate the proposed method.

Instantaneous frequency estimation of multi-component Chirp signals in noisy environments

A classical time-varying signal, the multi-component Chirp signal has been widely used and the ability to estimate its instantaneous frequency （IF） is very useful. But in noisy environments, it is hard to estimate the 1F of a multi-component Chirp signal accurately. Wigner distribution maxima （WDM） are usually utilized for this estimation. But in practice, estimation bias increases when some points deviate from the true IF in high noise environments. This paper presents a new method of multi-component Chirp signal 1F estimation named Wigner Viterbi fit （WVF）, based on Wigner-Ville distribution （WVD） and the Viterbi algorithm. First, we transform the WVD of the Chirp signal into digital image, and apply the Viterbi algorithm to separate the components and estimate their IF. At last, we establish a linear model to fit the estimation results. Theoretical analysis and simulation results prove that this new method has high precision and better performance than WDM in high noise environments, and better suppression of interference and the edge effect. Compared with WDM, WVF can reduce the mean square error （MSE） by 50% when the signal to noise ration （SNR） is in the range of-15dB to -11dB. WVF is an effective and promising 1F estimation method.

Switchable instantaneous frequency measurement by optical power monitoring based on DP-QPSK modulator

We propose and analyze an instantaneous frequency measurement system by using optical power monitoring technique with improved resolution.The primary component adopted in the proposal is a dual-polarization quadrature phase shift keying(DP-QPSK) modulator which is used to modulate the microwave signal that has a designed time delay and phase shifting.The generated optical signal is sent to polarization beam splitter(PBS) in DP-QPSK modulator.Owing to the complementary transmission nature of polarization interference introduced by PBS,the frequency information is converted into the optical power and the relationship between the amplitude comparison function(ACF) and microwave frequency to be measured is established.Thus,the frequency of the microwave signal can be easily measured through monitoring the optical powers of the two output ports of the PBS.Furthermore,by adjusting the direct current(DC) biases of the DP-QPSK modulator instead of changing the electrical delay,the measurement range and resolution can be switched.In this paper,the basic principle of the instantaneous frequency measurement system is derived in detail,and simulation has been performed to investigate the resolution,the measurement range,and the influence of imperfection devices.The proposed scheme is wavelength-independent and its measurement range is switchable,which can avoid the laser wavelength drifting problem and thus greatly increasing the system flexibility.

Signal Separation and Instantaneous Frequency Estimation Based on Multi-scale Chirplet Sparse Signal Decomposition

An approach based on multi-scale ehirplet sparse signal decomposition is proposed to separate the malti-component polynomial phase signals, and estimate their instantaneous frequencies. In this paper, we have generated a family of multi-scale chirplet functions which provide good local correlations of chirps over shorter time interval. At every decomposition stage, we build the so-called family of chirplets and our idea is to use a structured algorithm which exploits information in the family to chain chirplets together adaptively as to form the polyncmial phase signal component whose correlation with the current residue signal is largest. Simultaueously, the polynomial instantaneous frequency is estimated by connecting the linear frequency of the chirplet functions adopted in the current separation. Simulation experiment demonstrated that this method can separate the camponents of the multi-component polynamial phase signals effectively even in the low signal-to-noise ratio condition, and estimate its instantaneous frequency accurately.

Chip-scale Brillouin instantaneous frequency measurement by use of one-shot frequency-to-power mapping based on lock-in amplification

We demonstrate a chip-scale scheme of Brillouin instantaneous frequency measurement(IFM) in a CMOS-compatible doped silica waveguide chip. In the chip-scale Brillouin IFM scheme, the frequency-to-power mapping process is achieved by one-shot detection without additional time averaging and implemented by lock-in amplification, which successfully detects the Brillouin gain of the doped silica waveguide chip in the time domain. A Costas frequency modulated signal ranging from 8 GHz to 9 GHz is experimentally measured, and the frequency measurement errors are maintained within 58 MHz.

Efficacy of Hilbert-Huang Transform (HHT) in the Analysis of Instantaneous Low Frequency Waves of Magnetosheath

The flow of supersonic plasma is accompanied by a highly thermalized region called the Magnetoshealth found after the bow shock. Enclosed within this region are different wave modes associated with classes of boundaries which have been determined by different methods. The efficacy of Hilbert-Huang transform (HHT) is based on the conditionality of allowing for the local analysis of frequencies, which presents the physical meaning of the original signal at that instant. The observed data have been taken from Cluster II Fluxgate Magnetometer (FGM) instrument that provides advantage for the analysis in three dimensions. The result compares favourably with instantaneous frequencies computed using simple Hilbert transform (SHT) with electric field measurements of Cluster II mission already carried out in literatures. The result of this study has shown that HHT provides the best applicability in the magnetosheath data analysis than the wavelet and Fast Fourier Transform (FFT). The application of HHT based on its advantages over other methods is viewed to be very critical in the analysis of multi-frequency signals where different frequencies could be determined distinctively at a point.

Efficacy of Hilbert-Huang Transform (HHT) in the Analysis of Instantaneous Low Frequency Waves of Magnetosheath

The flow of supersonic plasma is accompanied by a highly thermalized region called the Magnetoshealth found after the bow shock. Enclosed within this region are different wave modes associated with classes of boundaries which have been determined by different methods. The efficacy of Hilbert-Huang transform (HHT) is based on the conditionality of allowing for the local analysis of frequencies, which presents the physical meaning of the original signal at that instant. The observed data have been taken from Cluster II Fluxgate Magnetometer (FGM) instrument that provides advantage for the analysis in three dimensions. The result compares favourably with instantaneous frequencies computed using simple Hilbert transform (SHT) with electric field measurements of Cluster II mission already carried out in literatures. The result of this study has shown that HHT provides the best applicability in the magnetosheath data analysis than the wavelet and Fast Fourier Transform (FFT). The application of HHT based on its advantages over other methods is viewed to be very critical in the analysis of multi-frequency signals where different frequencies could be determined distinctively at a point.

Rolling element bearing instantaneous rotational frequency estimation based on EMD soft-thresholding denoising and instantaneous fault characteristic frequency

The accurate estimation of the rolling element bearing instantaneous rotational frequency(IRF) is the key capability of the order tracking method based on time-frequency analysis. The rolling element bearing IRF can be accurately estimated according to the instantaneous fault characteristic frequency(IFCF). However, in an environment with a low signal-to-noise ratio(SNR), e.g., an incipient fault or function at a low speed, the signal contains strong background noise that seriously affects the effectiveness of the aforementioned method. An algorithm of signal preprocessing based on empirical mode decomposition(EMD) and wavelet shrinkage was proposed in this work. Compared with EMD denoising by the cross-correlation coefficient and kurtosis(CCK) criterion, the method of EMD soft-thresholding(ST) denoising can ensure the integrity of the signal, improve the SNR, and highlight fault features. The effectiveness of the algorithm for rolling element bearing IRF estimation by EMD ST denoising and the IFCF was validated by both simulated and experimental bearing vibration signals at a low SNR.

Adaptive Fourier Decomposition Based Time-Frequency Analysis

The attempt to represent a signal simultaneously in time and frequency domains is full of challenges. The recently proposed adaptive Fourier decomposition （AFD） offers a practical approach to solve this problem. This paper presents the principles of the AFD based time-frequency analysis in three aspects： instantaneous frequency analysis, frequency spectrum analysis, and the spectrogram analysis. An experiment is conducted and compared with the Fourier transform in convergence rate and short-time Fourier transform in time-frequency distribution. The proposed approach performs better than both the Fourier transform and short-time Fourier transform.

Application of formant instantaneous characteristics to speech recognition and speaker identification

This paper proposes a new phase feature derived from the formant instantaneous characteristics for speech recognition （SR） and speaker identification （SI） systems. Using Hilbert transform （HT）, the formant characteristics can be represented by instantaneous frequency （IF） and instantaneous bandwidth, namely formant instantaneous characteristics （FIC）. In order to explore the importance of FIC both in SR and SI, this paper proposes different features from FIC used for SR and SI systems. When combing these new features with conventional parameters, higher identification rate can be achieved than that of using Mel-frequency cepstral coefficients （MFCC） parameters only. The experiment results show that the new features are effective characteristic parameters and can be treated as the compensation of conventional parameters for SR and SI.

Seismic attribute extraction based on HHT and its application in a marine carbonate area

The Hilbert-Huang transform（HHT） is a new analysis method suitable for nonlinear and non-stationary signals.It is very appropriate to seismic signals because they show both non-stationary and nonlinear characteristics.We first introduce the realization of HHT empirical mode decomposition（EMD） and then comparatively analyze three instantaneous frequency algorithms based on intrinsic mode functions（IMF） resulting from EMD,of which one uses the average instantaneous frequency of two sample intervals having higher resolution which can determine that the signal frequency components change with time.The method is used with 3-D poststack migrated seismic data of marine carbonate strata in southern China to effectively extract the three instantaneous attributes.The instantaneous phase attributes of the second intrinsic mode functions（IMF2） better describe the reef facies of the platform margin and the IMF2 instantaneous frequency attribute has better zoning.Combining analysis of the three IMF2 instantaneous seismic attributes and drilling data can identify the distribution of sedimentary facies well.

Multi-Component Signal Processing for the Short Range Radar

To study the measurement of distance under the condition of the frequency modulation (FM) multi component signal of a short range radar, the multi points scattering model of a target, the TLS ESPRIT (total least square estimation of signal parameters via rotational invariance techniques) and the mathematical statistics methods were used. The method of computing single frequency signal's instantaneous frequency (IF) is unsuitable to the multi component signal. By using the method of the TLS ESPRIT combined with the mathematical statistics, the multi component signal's IF can be obtained. The computer simulation has shown that the method has the high accuracy for measuring the distance.

Recording-based identification of site liquefaction

Reconnaissance reports and pertinent research on seismic hazards show that liquefaction is one of the key sources of damage to geotechnical and structural engineering systems. Therefore, identifying site liquefaction conditions plays an important role in seismic hazard mitigation. One of the widely used approaches for detecting liquefaction is based on the time-frequency analysis of ground motion recordings, in which short-time Fourier transform is typically used. It is known that recordings at a site with liquefaction are the result of nonlinear responses of seismic waves propagating in the liquefied layers underneath the site. Moreover, Fourier transform is not effective in characterizing such dynamic features as time-dependent frequency of the recordings rooted in nonlinear responses. Therefore, the aforementioned approach may not be intrinsically effective in detecting liquefaction. An alternative to the Fourier-based approach is presented in this study, which proposes time-frequency analysis of earthquake ground motion recordings with the aid of the Hilbert-Huang transform （HHT）, and offers justification for the HHT in addressing the liquefaction features shown in the recordings. The paper then defines the predominant instantaneous frequency （PIF） and introduces the PiF-related motion features to identify liquefaction conditions at a given site. Analysis of 29 recorded data sets at different site conditions shows that the proposed approach is effective in detecting site liquefaction in comparison with other methods.

Wigner-Ville distribution and cross Wigner-Ville distribution of noisy signals

The Wigner-Ville distribution （WVD） and the cross Wigner-Ville distribution （XWVD） have been shown to be efficient in the estimation of instantaneous frequency （IF）. But the statistical result of the IF estimation from XWVD peak is much better than using WVD peak. The reason is given from a statistical point of view. Theoretical studies show that XWVD of the analyzed signal can be estimated from XWVD of the noise-contaminated signal. The estimation is unbiased, and the variance is equal to that of noise. In this case, WVD cannot be estimated from W-VD of the noise-contaminated signal. Therefore, higher SNR is required when WVD is used to analyze signals.

Improvement on polynomial Wigner-Ville distribution for detecting higher-order polynomial phase signal

To detect higher order polynomial phase signals （HOPPSs）, the smoothed-pseudo polynomial Wigner-Ville distribution （SP-PVCVD）, an improved version of the polynomial Wigner-Ville distribution （PVCVD）, is presented using a separable kernel. By adjusting the lengths of the functions in the kernel, the balance between resolution retaining and interference suppressing can be adjusted conveniently. The proposed method with merits of interference terms reduction and noise suppression can provide time frequency representation of better readability and more accurate instantaneous frequency （IF） estimation with higher order SP-PVfVD. The performance of the SP-PWVD is verified by computer simulations.