Ultrasonic transducer array tomography for detecting defect of metal plate based on Hilbert transformation

Hilbert transformation and improved ellipse localization method is applied in ultrasonic transducer array tomography to detect defect of metal plate.By combining the improved ellipse localization method and time-reversal method,the new ultrasonic tomography algorithm employs smooth Hilbert envelope instead of discrete amplitude to reconstruct defect image.An ultrasonic tomography system with six transducers is built to evaluate the effectiveness of the new ultrasonic tomography algorithm.The S0 mode Lamb wave is excited on special condition,and the mode of received signal is identified by Vigner-Wille distribution.The gray value of image area is defined by envelope of the reflected S0 mode Lamb wave signal from defect boundary.Defect image can be reconstructed by summing gray value of all pixels in the image area.The experimentally reconstructed defect image shows that the new tomography algorithm based on Hilbert transformation is efficient for defect detection in metal plate.

Quantum Mechanical Hilbert Transformation for Normally Ordering Coulomb Potential-Type Operators

We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.

Identification of nonlinear multi-degree-of freedom structures based on Hilbert transformation

The modeling method and identified method adapted to multi-degree-of-freedom structures with strucrural nonlinearities are established.The component mode synthesis method is used to establish the nonlinear governing equations by extending the connected relationships.Based on the modeling method,the Hilbert transform method is applied to identify the nonlinear stiffness of multi-degree-of-freedom structures.Nonlinear analysis and identification of a typical folding wing configuration with three freeplay hinges are investigated.The nonlinear governing equation is established based on present methods and the computing results of different stiffness are checked by finite element programming.In order to illustrate the influence of the nonlinearities,the frequency response characteristics of the structure are analyzed and Hilbert transform is performed.The Hilbert transform identification method is utilized to identify the nonlinear stiffness of nonlinear hinges in the time domain and several parametric studies are performed.In addition,the comparison of response is made to illustrate the feasibility of the methods.The results show that the extending component mode synthesis method in the present work can be used to establish the governing equation with structural nonlinearities.Based on the modeling method,the Hilbert transform identified method can be extended to multi-degree-of-freedom structures accurately.

Seismic dip estimation based on the twodimensional Hilbert transform and its application in random noise attenuation

In seismic data processing, random noise seriously affects the seismic data quality and subsequently the interpretation. This study aims to increase the signal-to-noise ratio by suppressing random noise and improve the accuracy of seismic data interpretation without losing useful information. Hence, we propose a structure-oriented polynomial fitting filter. At the core of structure-oriented filtering is the characterization of the structural trend and the realization of nonstationary filtering. First, we analyze the relation of the frequency response between two-dimensional（2D） derivatives and the 2D Hilbert transform. Then, we derive the noniterative seismic local dip operator using the 2D Hilbert transform to obtain the structural trend. Second, we select polynomial fitting as the nonstationary filtering method and expand the application range of the nonstationary polynomial fitting. Finally, we apply variableamplitude polynomial fitting along the direction of the dip to improve the adaptive structureoriented filtering. Model and field seismic data show that the proposed method suppresses the seismic noise while protecting structural information.

基于CEEMDAN-HT的永磁同步电机匝间短路振动信号故障特征提取研究

由于长时间处于高负荷运行状态,永磁同步电机(permanent magnet synchronous motor, PMSM)定子绕组线圈匝与匝之间的绝缘性能容易降低,导致出现匝间短路,此时电机的振动强度会发生改变。针对此现象,提出将自适应噪声完备经验模态分解(complete ensemble empirical mode decomposition with adaptive noise, CEEMDAN)与希尔伯特变换(Hilbert transform, HT)结合,构成一种CEEMDAN-HT非线性信号分析方法,并将其应用于提取振动信号故障特征。首先,利用CEEMDAN算法分解振动信号,得到一系列本征模态函数(intrinsic mode function, IMF),并将主元分析中的方差贡献率用于识别包含故障特征信息的IMF。其次,使用HT对方差贡献率较高的IMF进行分析,并以三维联合时频图呈现时间、瞬时频率与幅值,得到了主要故障特征。最后,使用ANSYS有限元软件建立了电机短路故障模型,并搭建了短路故障试验平台,通过对比有限元仿真结果与试验结果,对提出的方法进行了有效性和准确性验证。

Novel self-embedding holographic watermarking image encryption protection scheme

For digital image transmission security and information copyright,a new holographic image self-embedding watermarking encryption scheme is proposed.Firstly,the plaintext is converted to the RGB three-color channel,the corresponding phase hologram is obtained by holographic technology and the watermark is self-embedded in the frequency domain.Secondly,by applying the Hilbert transform principle and genetic center law,a complete set of image encryption algorithms is constructed to realize the encryption of image information.Finally,simulation results and security analysis indicate that the scheme can effectively encrypt and decrypt image information and realize the copyright protection of information.The introduced scheme can provide some support for relevant theoretical research,and has practical significance.

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.

Design of a Multifrequency Signal Parameter Estimation Method for the Distribution Network Based on HIpST

The application of traditional synchronous measurement methods is limited by frequent fluctuations of electrical signals and complex frequency components in distribution networks.Therefore,it is critical to find solutions to the issues of multifrequency parameter estimation and synchronous measurement estimation accuracy in the complex environment of distribution networks.By utilizing the multifrequency sensing capabilities of discrete Fourier transform signals and Taylor series for dynamic signal processing,a multifrequency signal estimation approach based on HT-IpDFT-STWLS(HIpST)for distribution networks is provided.First,by introducing the Hilbert transform(HT),the influence of noise on the estimation algorithm is reduced.Second,signal frequency components are obtained on the basis of the calculated signal envelope spectrum,and the interpolated discrete Fourier transform(IpDFT)frequency coarse estimation results are used as the initial values of symmetric Taylor weighted least squares(STWLS)to achieve high-precision parameter estimation under the dynamic changes of the signal,and the method increases the number of discrete Fourier.Third,the accuracy of this proposed method is verified by simulation analysis.Data show that this proposed method can accurately achieve the parameter estimation of multifrequency signals in distribution networks.This approach provides a solution for the application of phasor measurement units in distribution networks.

Dispersion Relations in Diffraction in Time

In agreement with Titchmarsh’s theorem, we prove that dispersion relations are just the Fourier-transform of the identity, g(x′)=±Sgn(x′)g(x′), which defines the property of being a truncated functions at the origin. On the other hand, we prove that the wave-function of a generalized diffraction in time problem is just the Fourier-transform of a truncated function. Consequently, the existence of dispersion relations for the diffraction in time wave-function follows. We derive these explicit dispersion relations.

WEIGHTED HILBERT TRANSFORM AND BαMETRIC

In the paper, the author generalized the Hardy and Littlewood's theorem toBa space, i.e. for all Pm satisfying 1 < α = infpm≤ β≤ suppm < ∞, m = 1, 2,..., and the following inequalityholds if and on1y if.

Hilbert Transferin Applied to Separation of Waves

The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is applicable to both regular and irregular trains; of waves. The wave data series measured with two wave gauges in the experiments are separated into two series of incident and reflected waves. Then, the reflection coefficient can be easily obtained. The arrival of reflected waves can also be detected for improvement of the accuracy of the reflection coefficient. The reflection performance of the physical model can be estimated exactly without calculation of wave height and phase difference. Numerical samples developed to test the method are proved to be accurate. Physical experiments are conducted and compared with Goda's method and satisfactory results are obtained.

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.

Condition Evaluation in Steel Truss Bridge with Fused Hilbert Transform,Spectral Kurtosis,and Bandpass Filter

This study is concerned with the diagnosis of discrepancies in a steel truss bridge by identifying dynamic properties from the vibration response signals of the bridges.The vibration response signals collected at bridges under three different vehicular speeds of 10 km/hr,20 km/hr,and 30 km/hr are analyzed using statistical features such as kurtosis,magnitude of peak-to-peak,root mean square,crest factor as well as impulse factor in time domain,and Stockwell transform in the time-frequency domain.The considered statistical features except for kurtosis show uncertain behavior.The Stockwell transform showed low-resolution outcomes when the presence of noise in the recorded vibration responses.The elimination of noise and extraction of meaningful dynamic properties from the vibration responses is done by applying a new method which comes from the fusion of Hilbert transform with Spectral kurtosis and bandpass filtering.The outcomes obtained from Hilbert transform processed residual signals which are further filtered using bandpass filter show more robustness and accuracy in characterizing bridge modal frequencies from the noisy vibration responses.The proposed method produces a high-resolution frequency response which can unveil the joint discrepancy in the bridge structure.

A Method for Incipient Fault Diagnosis of Roller Bearings Based on the Wavelet Transform Correlation Filter and Hilbert Transform

Noise is the biggest obstacle that makes the incipient fault diagnosis results of roller bearings uncorrected; a new method for diagnosing incipient fault of roller bearings based on the Wavelet Transform Correlation Filter and Hilbert Transform was proposed. First, the weak fault information features are picked up from the roller bearings fault vibration signals by use of a de-noising characteristic of the Wavelet Transform Correlation Filter as the preprocessing of the Hilbert Envelope Analysis. Then, in order to get fault features frequency, de-noised wavelet coefficients of high scales which represent high frequency signal were analyzed by Hilbert Envelope Spectrum Analysis. The simulation signals and diagnosing examples analysis results reveal that the proposed method is more effective than the method of direct wavelet coefficients-Hilbert Transform in de-noising and clarifying roller bearing incipient fault.

Phase Error Compensation of Three-Dimensional Reconstruction Combined with Hilbert Transform

Nonlinear response is an important factor affecting the accuracy of three-dimensional image measurement based on the fringe structured light method.A phase compensation algorithm combined with a Hilbert transform is proposed to reduce the phase error caused by the nonlinear response of a digital projector in the three-dimensional measurement system of fringe structured light.According to the analysis of the influence of Gamma distortion on the phase calculation,the algorithm establishes the relationship model between phase error and harmonic coefficient,introduces phase shift to the signal,and keeps the signal amplitude constant while filtering out the DC component.The phase error is converted to the transform domain,and compared with the numeric value in the space domain.The algorithm is combined with a spiral phase function to optimize the Hilbert transform,so as to eliminate external noise,enhance the image quality,and get an accurate phase value.Experimental results show that the proposed method can effectively improve the accuracy and speed of phase measurement.By performing phase error compensation for free-form surface objects,the phase error is reduced by about 26%,and about 27%of the image reconstruction time is saved,which further demonstrates the feasibility and effectiveness of the method.

Oscillatory hyper Hilbert transforms along curves

The hyper Hilbert transform Tnf（x） =∫-1^1 f（x - Γ（t））e^-i｜t｜-β｜t｜^-1-αdt along an appropriate curve Γ（t） on R^n is investigated,where β 〉 α 〉 0.An L^p boundedness theorem of T4 is obtained,which is an extension of some earlier results of n = 2 and n = 3.

Transient Power and Quality Events Analysed Using Hilbert Transforms

This work presents an advanced mathematical tool applicable to the recognition and classification of power system transients and disturbances. Disturbances without a periodic pattern or with a non-linear pattern require a more suitable tool than the Fourier series （Fast Fourier or Windowed Fourier Transforms）. To overcome these drawbacks, other tools have been broadly used, such as the wavelet transform. However, the wavelet transform also has some drawbacks such as the lack of adaptivity or interpretation of nonlinear phenomena that the Hilbert and Hilbert Huang Transform techniques could mitigate. The Hilbert techniques transform a time domain function into a space representation both in time and frequency. In the paper, the technique is applied to analyse several short-term and steady events, like a short circuit, a capacitor-switching transient, or a line energisation, showing the abilities of the Hilbert-based transforms.

A Double-Ended Protection Principle for an LCC-VSC-MTDC System with Strong Anti-Interference Ability

The DC grid technology of multi-power supply and multi-drop-point power reception is an effective solution for large-scale renewable energy integration into the power grid.Line-commutated converter-Voltage source converter(LCC-VSC)power grids are one of the more important developmental directions of the future power grid that have occured in recent years.But the multi-terminal high voltage direct current system has the problems of inconsistent boundary characteristics,inconsistent control,and fault response characteristics,which puts higher requirements on the protection scheme.Thus,a completely new protection principle is proposed in this paper.Firstly,the fault characteristics of distributed capacitance current are analyzed.The reactive power calculated by the distribution parameters of different frequencies is different.Subsequently,the fault characteristics of DC reactive power are analyzed,and a DC reactive power extraction algorithm is proposed.The polarity of the multi-band DC reactive power is used to construct the protection scheme.Finally,the LCC-VSC power grid model verifies the correctness and superiority of the proposed protection scheme.The proposed scheme uses DC reactive power instead of fault current to solve the long delay problem caused by distributed capacitance.Compared with the prior art,the proposed solution is not affected by distributed capacitance and has a stronger anti-interference ability(600Ω+10 dB+1 ms).

Cyclostationary Feature Detection Based Spectrum Sensing Algorithm under Complicated Electromagnetic Environment in Cognitive Radio Networks

This paper focuses on improving the detection performance of spectrum sensing in cognitive radio(CR) networks under complicated electromagnetic environment. Some existing fast spectrum sensing algorithms cannot get specific features of the licensed users'(LUs') signal, thus they cannot be applied in this situation without knowing the power of noise. On the other hand some algorithms that yield specific features are too complicated. In this paper, an algorithm based on the cyclostationary feature detection and theory of Hilbert transformation is proposed. Comparing with the conventional cyclostationary feature detection algorithm, this approach is more flexible i.e. it can flexibly change the computational complexity according to current electromagnetic environment by changing its sampling times and the step size of cyclic frequency. Results of simulation indicate that this approach can flexibly detect the feature of received signal and provide satisfactory detection performance compared to existing approaches in low Signal-to-noise Ratio(SNR) situations.

THE ACCOMPANIED SLOWLY-VARIANT-SYSTEM OF NONLINEAR DYNAMIC SYSTEMS

The slowly-variant-system is defined and analyzed in this paper and the nonlinear relationship between its instantaneous parameters and the instantaneous amplitude and frequency of its free vibration response is established. By defining the band-pass mapping, a slowly-variant-system which we call the accompanied slowly-variant-system is extracted from the nonlinear system; and the relationship between the two systems is discussed. Also, the skeleton curves that can illustrate the nonlinearity and the main properties of the nonlinear system directly and concisely are defined. Work done in this paper opens a new way for nonlinearity detection and identification for nonlinear systems.