The W transform and its improved methods for time-frequency analysis of seismic data

The conventional linear time-frequency analysis method cannot achieve high resolution and energy focusing in the time and frequency dimensions at the same time,especially in the low frequency region.In order to improve the resolution of the linear time-frequency analysis method in the low-frequency region,we have proposed a W transform method,in which the instantaneous frequency is introduced as a parameter into the linear transformation,and the analysis time window is constructed which matches the instantaneous frequency of the seismic data.In this paper,the W transform method is compared with the Wigner-Ville distribution(WVD),a typical nonlinear time-frequency analysis method.The WVD method that shows the energy distribution in the time-frequency domain clearly indicates the gravitational center of time and the gravitational center of frequency of a wavelet,while the time-frequency spectrum of the W transform also has a clear gravitational center of energy focusing,because the instantaneous frequency corresponding to any time position is introduced as the transformation parameter.Therefore,the W transform can be benchmarked directly by the WVD method.We summarize the development of the W transform and three improved methods in recent years,and elaborate on the evolution of the standard W transform,the chirp-modulated W transform,the fractional-order W transform,and the linear canonical W transform.Through three application examples of W transform in fluvial sand body identification and reservoir prediction,it is verified that W transform can improve the resolution and energy focusing of time-frequency spectra.

Time-frequency analysis of Li solid-phase diffusion in spherical active particles under typical discharge modes

Li transient concentration distribution in spherical active material particles can affect the maximum power density and the safe operating regime of the electric vehicles(EVs). On one hand, the quasiexact/exact solution obtained in the time/frequency domain is time-consuming and just as a reference value for approximate solutions;on the other hand, calculation errors and application range of approximate solutions not only rely on approximate algorithms but also on discharge modes. For the purpose to track the transient dynamics for Li solid-phase diffusion in spherical active particles with a tolerable error range and for a wide applicable range, it is necessary to choose optimal approximate algorithms in terms of discharge modes and the nature of active material particles. In this study, approximation methods,such as diffusion length method, polynomial profile approximation method, Padé approximation method,pseudo steady state method, eigenfunction-based Galerkin collocation method, and separation of variables method for solving Li solid-phase diffusion in spherical active particles are compared from calculation fundamentals to algorithm implementation. Furthermore, these approximate solutions are quantitatively compared to the quasi-exact/exact solution in the time/frequency domain under typical discharge modes, i.e., start-up, slow-down, and speed-up. The results obtained from the viewpoint of time-frequency analysis offer a theoretical foundation on how to track Li transient concentration profile in spherical active particles with a high precision and for a wide application range. In turn, optimal solutions of Li solid diffusion equations for spherical active particles can improve the reliability in predicting safe operating regime and estimating maximum power for automotive batteries.

Novel Doppler Frequency Extraction Method Based on Time-Frequency Analysis and Morphological Operation

A novel method of Doppler frequency extraction is proposed for Doppler radar scoring systems. The idea is that the time-frequency map can show how the Doppler frequency varies along the time-line, so the Doppler frequency extraction becomes curve detection in the image-view. A set of morphological operations are used to implement curve detection. And a map fusion scheme is presented to eliminate the influence of strong direct current （DC） component of echo signal during curve detection. The radar real-life data are used to illustrate the performance of the new approach. Experimental results show that the proposed method can overcome the shortcomings of piecewise-processing-based FFT method and can improve the measuring precision of miss distance.

Stability analysis of a liquid crystal elastomer self-oscillator under a linear temperature field

Self-oscillating systems abound in the natural world and offer substantial potential for applications in controllers,micro-motors,medical equipments,and so on.Currently,numerical methods have been widely utilized for obtaining the characteristics of self-oscillation including amplitude and frequency.However,numerical methods are burdened by intricate computations and limited precision,hindering comprehensive investigations into self-oscillating systems.In this paper,the stability of a liquid crystal elastomer fiber self-oscillating system under a linear temperature field is studied,and analytical solutions for the amplitude and frequency are determined.Initially,we establish the governing equations of self-oscillation,elucidate two motion regimes,and reveal the underlying mechanism.Subsequently,we conduct a stability analysis and employ a multi-scale method to obtain the analytical solutions for the amplitude and frequency.The results show agreement between the multi-scale and numerical methods.This research contributes to the examination of diverse self-oscillating systems and advances the theoretical analysis of self-oscillating systems rooted in active materials.

Parameterized time-frequency analysis to separate multi-radar signals

Multi-radar signal separation is a critical process in modern reconnaissance systems. However, the complicated battlefield is typically confronted with increasing electronic equipment and complex radar waveforms. The intercepted signal is difficult to separate with conventional parameters because of severe overlapping in both time and frequency domains. On the contrary, time-frequency analysis maps the 1D signal into a 2D time-frequency plane, which provides a better insight into the signal than traditional methods. Particularly, the parameterized time-frequency analysis (PTFA) shows great potential in processing such non stationary signals. Five procedures for the PTFA are proposed to separate the overlapped multi-radar signal, including initiation, instantaneous frequency estimation with PTFA, signal demodulation, signal separation with adaptive filter and signal recovery. The proposed method is verified with both simulated and real signals, which shows good performance in the application on multi-radar signal separation.

Early detection of sudden cardiac death by using classical linear techniques and time-frequency methods on electrocardiogram signals

Early detection of sudden cardiac death may be used for surviving the life of cardiac patients. In this paper we have investigated an algorithm to detect and predict sudden cardiac death, by processing of heart rate variability signal through the classical and time-frequency methods. At first, one minute of ECG signals, just before the cardiac death event are extracted and used to compute heart rate variability (HRV) signal. Five features in time domain and four features in frequency domain are extracted from the HRV signal and used as classical linear features. Then the Wigner Ville transform is applied to the HRV signal, and 11 extra features in the time-frequency (TF) domain are obtained. In order to improve the performance of classification, the principal component analysis (PCA) is applied to the obtained features vector. Finally a neural network classifier is applied to the reduced features. The obtained results show that the TF method can classify normal and SCD subjects, more efficiently than the classical methods. A MIT-BIH ECG database was used to evaluate the proposed method. The proposed method was implemented using MLP classifier and had 74.36% and 99.16% correct detection rate (accuracy) for classical features and TF method, respectively. Also, the accuracy of the KNN classifier were 73.87% and 96.04%.

A Recursive Method of Time-Frequency Analysis for the Signal Processing of Flutter Test with Progression Variable Speed

Focused on the non-statlonarity and real-time analysis of signal in flutter test with progression variable speed （FTPVS）, a new method of recursive time-frequency analysis is presented. The time-varying system is tracked on-line by building a time-varying parameter model, and then the relevant parameter spectrum can be obtained. The feasibility and advantages of the method are examined by digital simulation. The results of FTPVS at low-speed wind-tunnel promise the engineering application perspective of the method.

NEW SAR IMAGE INTERPRETATION METHOD OF AIRCRAFT BASED ON JOINT TIME-FREQUENCY ANALYSIS

With the continuous improvement of Synthetic Aperture Radar(SAR) resolution, interpreting the small targets like aircraft in SAR images becomes possible and turn out to be a hot spot in SAR application research. However, due to the complexity of SAR imaging mechanism, interpreting targets in SAR images is a tough problem. This paper presents a new aircraft interpretation method based on the joint time-frequency analysis and multi-dimensional contrasting of basic structures. Moreover, SAR data acquisition experiment is designed for interpreting the aircraft. Analyzing the experiment data with our method, the result shows that the proposed method largely makes use of the SAR data information. The reasonable results can provide some auxiliary support for the SAR images manual interpretation.

Time-Frequency Analysis of EEG Signals Evoked by Voluntary, Stimulated and Imaginary Motions

In order to investigate the characteristics of sensorimotor cortex during motor execution(ME), voluntary, stimulated and imaginary finger flexions were performed by ten volunteer subjects. Electroencephalogram(EEG) data were recorded according to the modified 10-20 International EEG System. The patterns were compared by the analysis of the motion-evoked EEG signals focusing on the contralateral(C3) and ipsilateral(C4) channels for hemispheric differences. The EEG energy distributions at alpha(8—13 Hz), beta(14—30 Hz) and gamma(30—50 Hz) bands were computed by wavelet transform(WT) and compared by the analysis of variance(ANOVA). The timefrequency(TF) analysis indicated that there existed a contralateral dominance of alpha post-movement event-related synchronization(ERS) pattern during the voluntary task, and that the energy of alpha band increased in the ipsilateral area during the stimulated(median nerve of wrist) task. Besides, the contralateral alpha and beta event-related desynchronization(ERD) patterns were observed in both stimulated and imaginary tasks. Another significant difference was found in the mean power values of gamma band(p<0.01)between the imaginary and other tasks. The results show that significant hemispheric differences such as alpha and beta band EEG energy distributions and TF changing phenomena(ERS/ERD) were found between C3 and C4 areas during all of the three patterns. The largest energy distribution was always at the alpha band for each task.

IDENTIFICATION OF NONLINEAR DYNAMIC SYSTEMS:TIME-FREQUENCY FILTERING AND SKELETON CURVES

The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.

The combined time-frequency analysis of the acoustic signals backscattered from ultrasonic contrast agents in the evaluation of the blood perfusion

Objective: To analyze the non-periodic, unstable and even chaotic echoes scattered from microbubbles which are extremely sensitive and may easily collapse, fragment or shrink when ultrasound contrast agents are exposed to ultrasound (US) irradiation. Methods: The combined time-frequency analysis was applied to the original signals instead of the traditional Fourier spectral analysis technique. Results: The results obtained from simulation as well as experiment showed that the subharmonic, 2nd harmonic and ultra harmonic of the microbubbles occurred during the oscillation and varied with time. The dependence on the incident ultrasonic amplitude and microbubble parameters were established. Conclusion: The transient echoes backscattered from the ultrasound agent in the evaluation of the blood perfusion can be analyzed thoroughly by the technique of combined-frequency analysis and the time detail of the frequency contents can be revealed.

Time-Frequency Analysis of Asymmetric Triaxial Galaxy Model Including Effect of Spherical Dark Halo Component

A method of time-frequency analysis (TFA) based on wavelets is applied to study the phase space structure of three-dimensional asymmetric triaxial galaxy enclosed by spherical dark halo component. The investigation is carried out in the presence and absence of dark halo component. Time-frequency analysis is based on the extraction of instantaneous frequency from the phase of the continuous wavelet transform. This method is comparatively fast and reliable. This method can differentiate periodic from quasi-periodic, chaotic sticky from chaotic non-sticky, ordered from chaotic and also, it can accurately determine the time interval of the resonance trapping and transitions too. Apart from that, the phenomenon of transient chaos can be explained with the help of time-frequency analysis. Comparison with the method of total angular momentum (denoted as Ltot) proposed recently is also presented.

Application of Wavelet Packet De-noising in Time-Frequency Analysis of the Local Wave Method

The local wave method is a very good time-frequency method for nonstationaryvibration signal analysis. But the interfering noise has a big influence on the accuracy oftime-frequency analysis. The wavelet packet de-noising method can eliminate the interference ofnoise and improve the signal-noise-ratio. This paper uses the local wave method to decompose thede-noising signal and perform a time-frequency analysis. We can get better characteristics. Finally,an example of wavelet packet de-noising and a local wave time-frequency spectrum application ofdiesel engine surface vibration signal is put forward.

Time Series-, Time-Frequency- and Spectral Analyses of Sensor Measurements in an Offshore Wave Energy Converter Based on Linear Generator Technology

Inside the second experimental wave energy converter (WEC) launched at the Lysekil research site on the Swedish west coast in March 2009 a number of sensor systems were installed for measuring the mechanical performance of the WEC and its mechanical subsystems. One of the measurement systems was a set-up of 7 laser triangulation sensors for measuring relative displacement of the piston rod mechanical lead-through transmission in the direct drive. Two measurement periods, separated by 2.5 month, are presented in this paper. One measurement is made two weeks after launch and another 3 months after launch. Comparisons and correlations are made between different sensors measuring simultaneously. Noise levels are investigated. Filtering is discussed for further refinement of the laser triangulation sensor signals in order to separate noise from actual physical displacement and vibration. Measurements are presented from the relative displacement of the piston rod mechanical lead-through, from magnetic flux in the air gap, mechanical strain in the WEC structure, translator position and piston rod axial displacement and active AC power. Investigation into the measurements in the time domain with close-ups, in the frequency domain with Fast Fourier transform (FFT) and with time-frequency analysis with short time Fourier transform (STFT) is carried out to map the spectral content in the measurements. End stop impact is clearly visible in the time-frequency analysis. The FFT magnitude spectra are investigated for identifying the cogging bandwidth among other vibrations. Generator cogging, fluctuations in the damping force and in the Lorenz forces in the stator are distinguished and varies depending on translator speed. Vibrations from cogging seem to be present in the early measurement period while not so prominent in the late measurement period. Vibration frequencies due to wear are recognized by comparing with the noise at generator standstill and the vibration sources in the generator. It is concluded that a moving average is a sufficient filter in the time domain for further analysis of the relative displacement of the piston rod mechanical lead-through transmission.

Application of sparse time-frequency decomposition to seismic data

The Gabor and S transforms are frequently used in time-frequency decomposition methods. Constrained by the uncertainty principle, both transforms produce low-resolution time-frequency decomposition results in the time and frequency domains. To improve the resolution of the time-frequency decomposition results, we use the instantaneous frequency distribution function（IFDF） to express the seismic signal. When the instantaneous frequencies of the nonstationary signal satisfy the requirements of the uncertainty principle, the support of IFDF is just the support of the amplitude ridges in the signal obtained using the short-time Fourier transform. Based on this feature, we propose a new iteration algorithm to achieve the sparse time-frequency decomposition of the signal. The iteration algorithm uses the support of the amplitude ridges of the residual signal obtained with the short-time Fourier transform to update the time-frequency components of the signal. The summation of the updated time-frequency components in each iteration is the result of the sparse timefrequency decomposition. Numerical examples show that the proposed method improves the resolution of the time-frequency decomposition results and the accuracy of the analysis of the nonstationary signal. We also use the proposed method to attenuate the ground roll of field seismic data with good results.

Intelligibility evaluation of enhanced whisper in joint time-frequency domain

Some factors influencing the intelligibility of the enhanced whisper in the joint time-frequency domain are evaluated. Specifically, both the spectrum density and different regions of the enhanced spectrum are analyzed. Experimental results show that for a spectrum of some density, the joint time-frequency gain-modification based speech enhancement algorithm achieves significant improvement in intelligibility. Additionally, the spectrum region where the estimated spectrum is smaller than the clean spectrum, is the most important region contributing to intelligibility improvement for the enhanced whisper. The spectrum region where the estimated spectrum is larger than twice the size of the clean spectrum is detrimental to speech intelligibility perception within the whisper context.

Effects of Gabor transform parameters on signa time-frequency resolution

In this paper, it is described that the time-frequency resolution of geophysical signals is affected by the time window function attenuation coefficient and sampling interval and how such effects are eliminated effectively. Improving the signal resolution is the key to signal time-frequency analysis processing and has wide use in geophysical data processing and extraction of attribute parameters. In this paper, authors research the effects of the attenuation coefficient choice of the Gabor transform window function and sampling interval on signal resolution. Unsuitable parameters not only decrease the signal resolution on the frequency spectrum but also miss the signals. It is essential to first give the optimum window and range of parameters through time-frequency analysis simulation using the Gabor transform. In the paper, the suggestions about the range and choice of the optimum sampling interval and processing methods of general seismic signals are given.

Isolated Area Load Forecasting using Linear Regression Analysis: Practical Approach

This paper presents an analysis to forecast the loads of an isolated area where the history of load is not available or the history may not represent the realistic demand of electricity. The analysis is done through linear regression and based on the identification of factors on which electrical load growth depends. To determine the identification factors, areas are selected whose histories of load growth rate known and the load growth deciding factors are similar to those of the isolated area. The proposed analysis is applied to an isolated area of Bangladesh, called Swandip where a past history of electrical load demand is not available and also there is no possibility of connecting the area with the main land grid system.

Time-Frequency Characteristics of the Relationships Between Tropical Indo-Pacific SSTs

In this study, several advanced analysis methods are applied to understand the relationships between the Nino-3.4 sea surface temperatures （SST） and the SSTs related to the tropical Indian Ocean Dipole （IOD）. By analyzing a long data record, the authors focus on the time-frequency characteristics of these relationships, and of the structure of IOD. They also focus on the seasonal dependence of those characteristics in both time and frequency domains. Among the Nino-3.4 SST, IOD, and SSTs over the tropical western Indian Ocean （WIO） and eastern Indian Ocean （EIO）, the WIO SST has the strongest annual and semiannual oscillations. While the Nino-3.4 SST has large inter-annual variability that is only second to its annual variability, the IOD is characterized by the largest semiannual oscillation, which is even stronger than its annual oscillation. The IOD is strongly and stably related to the EIO SST in a wide range of frequency bands and in all seasons. However, it is less significantly related to the WIO SST in the boreal winter and spring. There exists a generally weak and unstable relationship between the WIO and EIO SSTs, especially in the biennial and higher frequency bands. The relationship is especially weak in summer and fall, when IOD is apparent, but appears highly positive in winter and spring, when the IOD is unimportantly weak and even disappears. This feature reflects a caution in the definition and application of IOD. The Nino-3.4 SST has a strong positive relationship with the WIO SST in all seasons, mainly in the biennial and longer frequency bands. However, it shows no significant relationship with the EIO SST in summer and fall, and with IOD in winter and spring.

μ ANALYSIS AND μ SYNTHESIS FOR NONLINEAR ROBUST CONTROL SYSTEMS

A μ analysis and μ synthesis method for nonlinear robust control systems was presented. The nonlinear robust contrl problem using μ method was described. By means of the nonlinear state feedback and state coordinates transformation, many uncertain nonlinear systems can be transformed as a linear fractional transformation (LFT) on the generalized plant and the uncertainty. Based on the LFT, a linear robust controller can be obtained by the DK iteration and then a corresponding nonlinear robust control law is constructed. An example was given in the paper.