Optimization of the End Effect of Hilbert-Huang transform(HHT)

In fault diagnosis of rotating machinery, Hil- bert-Huang transform （HHT） is often used to extract the fault characteristic signal and analyze decomposition results in time-frequency domain. However, end effect occurs in HHT, which leads to a series of problems such as modal aliasing and false IMF （Intrinsic Mode Func- tion）. To counter such problems in HHT, a new method is put forward to process signal by combining the general- ized regression neural network （GRNN） with the bound- ary local characteristic-scale continuation （BLCC）. Firstly, the improved EMD （Empirical Mode Decompo- sition） method is used to inhibit the end effect problem that appeared in conventional EMD. Secondly, the gen- erated IMF components are used in HHT. Simulation and measurement experiment for the cases of time domain, frequency domain and related parameters of Hilbert- Huang spectrum show that the method described here can restrain the end effect compared with the results obtained through mirror continuation, as the absolute percentage of the maximum mean of the beginning end point offset and the terminal point offset are reduced from 30.113% and 27.603% to 0.510% and 6.039% respectively, thus reducing the modal aliasing, and eliminating the false IMF components of HHT. The proposed method caneffectively inhibit end effect, reduce modal aliasing and false IMF components, and show the real structure of signal components accuratelX.

Mitigating end effects of EMD using non-equidistance grey model

Aiming at mitigating end effects of empirical mode decomposition （EMD）, a new approach motivated by the non- equidistance grey model （NGM） termed as NGM（1,1） is proposed. Other than trapezoid formulas, the cubic Hermite spline is put forward to improve the accuracy of derivative to the accumulated generating operation （AGO） series. Hopefully, it is worth stressing that the proposed NGM（1,1） model is particularly useful for predicting uncertainty data. Qualitative and quantitative comparisons between the proposed approach and other well-known algorithms are carried out through computer simulations on synthetic as well as natural signals. Simulation results demonstrate the proposed method can reduce end effects and improve the decomposition results of EMD.

A method for constraining the end effect of EMD based on sequential similarity detection and adaptive filter

Aimed at the problem of the end effect when using empirical mode decomposition(EMD),a method for constraining the end effect of EMD is proposed based on sequential similarity detection and adaptive filter.The method divides the signal into many wavelets,and it changes the initial wavelet length to select the best initial wavelet that has the minimum error and maximum number of matching seed wavelets,and the wavelet slopes are used for pre-matching and secondary matching to speed up the matching speed.Then,folded self-adaptive threshold is used to select multiple seed wavelets,and finally the end waveform is predicted and expanded according to the adaptive filter method.The proposed method is used to analyze the non-stationary nonlinear simulation signal and experimental signal,and it is compared with the mirror extension and RBF extension methods.The orthogonality index and similarity index of the EMD results of the extended signal after the proposed method are better than those of the other methods.The results show that the proposed method can better constrain the end effect,and has certain validity,accuracy and stability in solving the end effect problem.

Performance Analysis of Nested-loop Secondary Linear Doubly-fed Machine Considering End Effects

Nested-loop secondary linear doubly-fed machine(NLS-LDFM) is a novel linear machine evolved from rotary brushless doubly-fed induction machine, which has a good application prospect in linear metro. In order to analyze the performance of NLS-LDFM, the mechanism and action rules of end effects are investigated in this paper. Firstly, the mechanism of static and dynamic end effects is analyzed in aspect of direct coupling, winding asymmetry and transient secondary current. Furthermore, based on the winding theory for short primary linear machines, the machine parameters are established qualitatively considering pulsating magnetic field of NLS-LDFM. Finally, the NLS-LDFM performance analysis is supplemented by the finite element algorithm(FEA) simulation and experiments under different operating conditions.

A new method to reduce end effect of linear induction motor

A new method to compensate the end effect of a linear induction motor （LIM） in low-speed maglev vehicles is proposed. With this method, the motors are close to each other so that the front motor＇s exit-end magnetic field extends into the next motor＇s entry zone. As a result, the motor＇s magnetic field traveling wave become continuous and the end effect of short primary LIMs is greatly weakened. In the analysis of the air-gap magnetic field distribution, the LIM is assumedly divided into two identical motors vcith the distances of 20, 40, 60, and gO ram. The results show that the air-gap magnetic field is still continuous within these distances due to LIM＇s end effect. As the distance between two motors increases, the distortion of the air-gap magnetic field becomes more severe. Then, we investigate the relationship between the secondary speed and the thrust in three cases, i.e., a single LIM, two motors divided with 72 mm with pole pitch corrected, and two motors divided with 60 mm without the pole pitch being corrected. We find that the thrust has a small decrease when the speed increases, which means that the magnetic field is already continuous and its amplitude is approximately a constant. Furthermore, the thrust loss of case 3 is more than that of case 2, which indicates that the pole pitch correction is effective.

Polar motion prediction using the combination of SSA and ARMA

High-precision polar motion(PM) prediction is of important significance in astronomy, geodesy, aviation,hydrographic mapping, interstellar navigation, and so on. SSA can effectively extract the trend and period terms of PM,in the process of achieving high-precision medium-and long-term polar motion prediction,it is necessary to solve the end effect problem and overfitting problem of SSA forecasting method;therefore, ARMA was applied to decreasethe end effect, and a suitable combination of reconstructed components was determined to avoid the high variance reaction of SSA overfitting. Based on the decomposition and reconstruction of the PM by SSA, the reconstructed components are determined to participate in the SSA iterative fitting model according to the variance contribution rate. The combination of the reconstructed components representing the polar motion period term and the trend term is determined according to the correlation analysis of the selected reconstructed components. After the above work, the principal component prediction sequence is obtained by fitting the period term and the trend term to convergence, respectively, and then, the SSA end effect is modified, and the residual term is predicted based on ARMA. The test results show that he prediction accuracy of SSA + ARMA at the front of the X and Y directions are improved by 96.90% and 97.53% compared with those of SSA, respectively,and the forecast accuracy of 365 days are improved by 37.93% and 19.53% in the X and Y directions compared with those of Bulletin A, respectively.

Intelligent Diagnosis of Short Hydraulic Signal Based on Improved EEMD and SVM with Few Low-dimensional Training Samples

The high accurate classification ability of an intelligent diagnosis method often needs a large amount of training samples with high-dimensional eigenvectors, however the characteristics of the signal need to be extracted accurately. Although the existing EMD（empirical mode decomposition） and EEMD（ensemble empirical mode decomposition） are suitable for processing non-stationary and non-linear signals, but when a short signal, such as a hydraulic impact signal, is concerned, their decomposition accuracy become very poor. An improve EEMD is proposed specifically for short hydraulic impact signals. The improvements of this new EEMD are mainly reflected in four aspects, including self-adaptive de-noising based on EEMD, signal extension based on SVM（support vector machine）, extreme center fitting based on cubic spline interpolation, and pseudo component exclusion based on cross-correlation analysis. After the energy eigenvector is extracted from the result of the improved EEMD, the fault pattern recognition based on SVM with small amount of low-dimensional training samples is studied. At last, the diagnosis ability of improved EEMD＋SVM method is compared with the EEMD＋SVM and EMD＋SVM methods, and its diagnosis accuracy is distinctly higher than the other two methods no matter the dimension of the eigenvectors are low or high. The improved EEMD is very propitious for the decomposition of short signal, such as hydraulic impact signal, and its combination with SVM has high ability for the diagnosis of hydraulic impact faults.

Optimal design of auxiliary-teeth to solve circulation current reduction of permanent magnet linear synchronous motor

A discontinuity of magnetic circuits according to the end effect is generated in the permanent magnet linear synchronous motor （PMLSM）. Due to the unbalanced back electro-motive force （EMF） and impedance produced, unbalanced current is generated. The cireulatin8 current, which is caused by a decrease in the thrust, is generated by the unbalanced current. The optimal design of auxiliary-teeth at the end of the mover was carried out to solve the unbalance of phase by using design of experiment （DOE）, and compared with the basic model through finite element analysis （FEA）. As a result, the auxiliary-teeth model compensates for the decrease of thrust caused by the unbalanced phase. Also, this model is proven to reduce the detent force by the vibration and noise of the PMLSM and copper loss caused by the circulating current.

Single neuron network PI control of high reliability linear induction motor for Maglev

The paper deals with a new model of linear induction motor (LIM) to improve the reliability of the system. Based on the normal equation circuit of LIM considering the dynamic end effect, an equivalent circuit model with compensation of large end effect is constructed when the end effect force at synchronism is of braking character. The equivalent circuit model is used for secondary-flux oriented control of LIM. Single neuron network PI unit for LIM servo-drive is also discussed. The effectiveness of mathematical model for drive control is verified by simulations.

Stress and Displacement Distribution of Soft Clay Slope with 2D and 3D Elastoplastic Finite Element Method

Based on elastoplastic model, 2D and 3D finite element method （FEM） are used to calculate the stress and displacement distribution in the soft clay slope under gravity and uniform load at the slope top. Stability analyses indicate that 3D boundary effect varies with the stress level of the slope. When the slope is stable, end effect of 3D space is not remarkable. When the stability decreases, end effect occurs; when the slope is at limit state, end effect reaches maximum. The energy causing slope failure spreads preferentially along y-z section, and when the failure resistance capability reaches the limit state, the energy can extend along x-axis direction. The 3D effect of the slope under uniform load on the top is related to the ratio of load influence width to slope height, and the effect is remarkable with the decrease of the ratio.

Design strategy for detent force reduction of permanent magnet linear synchronous motor

The detent force of a permanent magnet linear synchronous motor （PMLSM） is analyzed and the corresponding optimization methods are presented to reduce it. The detent force, which is divided into two components, i.e. resulting from the end effect and resulting from the slotting effect, can be analyzed respectively by the finite element method （FEM）. To reduce the detent force arising from the end effect, several optimal design techniques are utilized, namely, adopting the suitable length and end shape of the primary armature. The detent force resulting from the slotting effect is reduced by means of skewing and adjusting the width of the magnets mounted on the secondary armature, and adopting the fractional slots of the primary armature. The validity of the analytical detent force predictions and the effectiveness of the detent force reduction techniques are verified by the experimental measurements.

Visualization study on fluid distribution and end effects in core flow experiments with low-field mri method

Core flow experiment is an important means of simulation experiments to evaluate the effect of displacing agent, but conventionally the internal characteristics in the core cannot be intuitively observed, and then some important information can not be directly acquired by experiments. In this paper, a visualization method was used to detect the water-flooding process by using an improved low field nuclear magnetic resonance imaging（MRI） device, and the images describing the distribution of oil and water were collected. The experimental results show that the distribution of oil and water can be visually detected in an appropriate range of core porosity, and the end effect in many mechanics experiments is found to exist also in natural core flow test, and the influence range is about 0.004 m from the end of a 0.05752 m length natural core. The results also indicate that MRI is an effective tool to study the real time fluid distribution in natural core.

DECAY RATE OF SAINT-VENANT END EFFECTS FOR PLANE DEFORMATIONS OF PIEZOELECTRIC-PIEZOMAGNETIC SANDWICH STRUCTURES

This paper is concerned with the decay of Saint-Venant end effects for plane deformations of piezoelectric （PE）-piezomagnetic （PM） sandwich structures, where a PM layer is located between two PE layers with the same material properties or reversely. The end of the sandwich structure is subjected to a set of self-equilibrated magneto-electro-elastic loads. The upper and lower surfaces of the sandwich structure axe mechanically free, electrically open or shorted as well as magnetically open or shorted. Firstly the constitutive equations of PE mate- rials and PM materials for plane strain are given and normalized. Secondly, the simplified state space approach is employed to arrange the constitutive equations into differential equations in a matrix form. Finally, by using the transfer matrix method, the characteristic equations for eigen- values or decay rates axe derived. Based on the obtained characteristic equations, the decay rates for the PE-PM-PE and PM-PE-PM sandwich structures are calculated. The influences of the electromagnetic boundary conditions, material properties of PE layers and volume fraction on the decay rates are discussed in detail.

Detection of Site-dependent Segmental Mobility of Polymer by Fluorescent Defocused Imaging

Polymer chain ends play an important role in the glassy dynamics of polymeric materials. In this study, a combination of single molecule defocus fluorescence microscopy and well-controlled atom transfer radical polymerization was used to investigate site-dependent segmental mobility of poly（n-butyl methacrylate）. As the temperature increased, the rotation of fluorophores, which were selectively labelled in chain end and chain middle, was gradually activated. The power spectra of rotation trajectories, the distribution of angular displacement as well as the population of rotating fluorophores demonstrated that the local dynamics was more activated at the chain ends than the middles, showing the unique contribution of the chain end to the dynamics of the system.

New insights into the effects of molecular weight and end group on the temperature-induced phase transition of poly(N-isopropylacrylamide) in water

In an attempt to clarify issues related to the molecular weight dependence of the phase transition of poly(N-isopropylacrylamide) (PNIPAM) in water,we prepared a library of PNIPAM samples of well-controlled molecular weight (7000 to 45000 g/mol) bearing identical groups on each chain end.The polymers were synthesized by reversible addition-fragmentation chain transfer (RAFT) polymerization of N-isopropylacrylamide (NIPAM) with a bifunctional chain tranfer agent and further end group modification.The effects of the end group chemical structure,hydroxyethyl (HE),propargyl (Pr),chloroethyl (CE),n-butyl (nBu),n-hexyl (nHe),and isobutylsulfanylthiosulfanyl (IBS) on the phase transition temperature of aqueous PNIPAM solutions were investigated by high-sensitivity differential scanning calorimetry (HS-DSC),yielding the enthalpy ΔH and the endotherm maximum temperature (T M),and turbidimetry,providing the cloud point (T CP) of each solution.The T CP and T M of the PNIPAM sample of lowest molar mass (M n 7,000 g/mol,0.5 g/L) ranged,respectively,from 38.8 to 22.5 °C and 42.2 to 26.0 °C,depending on the structure of the end-group,whereas H showed no strong end-group dependence.The phase transition of all polymers,except,-di(n-butyl-PNIPAM),exhibited a marked dependence on the polymer molar mass.

Highly rarefied gas flows in rough channels of finite length

Highly rarefied gas flows through a rough channel of finite length with small bumps appended to its surfaces are investigated,by varying the accommodation coefficientin Maxwell’s diffuse-specular boundary condition,the characteristic size and position of the bumps,and the channel length.First,we study the influence of the surface bumps and consider the rarefied gas flow in a unit channel with periodic boundary conditions to remove the end effect.It is found that the surface bumps have a significant impact on the flow permeability.Whenis very small(i.e.,nearly specular reflection of gas molecules at the channel surface),the apparent gas permeability is dramatically reduced,even in the presence of small bumps,to a value that is almost comparable to the one when fully diffuse gas-surface scattering is assumed.This impact can be taken into account through an effective accommodation coefficient,i.e.,the permeability of the rough channel is taken equivalently as that of a smooth channel without bumps but having gas-surface scattering under the effective accommodation coefficient.Second,we study the end effect by connecting a smooth channel of length L_(0) to two huge gas reservoirs.It is found that(i)the end correction length is large at small.Consequently,the mass flow rate barely reduces with increasing L_(0) rather than scales down by a factor of 1/L_(0) as predicted by the classical Knudsen diffusion theory;and(ii)the end correction is related to the channel’s aspect ratio.Finally,based on the effective accommodation coefficient and end correction,we explain the exotic flow enhancement in graphene angstrom-scale channels observed by Geim’s research group(Keerthi et al,Nature 558:420-424,2018).

Hilbert-Huang transform with adaptive waveform matching extension and its application in power quality disturbance detection for microgrid

With the significant improvement of microgrid technology, microgrid has gained large-scale application.However, the existence of intermittent distributed generations, nonlinear loads and various electrical and electronic devices causes power quality problem in microgrid, especially in islanding mode. An accurate and fast disturbance detection method which is the premise of power quality control is necessary. Aiming at the end effect and the mode mixing of original Hilbert-Huang transform(HHT), an improved HHT with adaptive waveform matching extension is proposed in this paper. The innovative waveform matching extension method considers not only the depth of waveform, but also the rise time and fall time. Both simulations and field experiments have verified the correctness and validity of the improved HHT for power quality disturbance detection in microgrid.

Internal wave parameter inversion based on Empirical Mode Decomposition

Wind, the result of earth rotation and other processes,inaugurate the phenomenon of oceanic internal waves（OIWs）, including driving turbulence, affecting nutrient and biomass distribution, and resuspending sediment. Therefore, a good understanding to OIWs＇ characters becomes a vital component to enhance its monitoring and utilization. The parameter inversion was conducted in the article for the OIW based on the empirical mode decomposition（EMD） method. The experimental data, the advanced synthetic aperture radar（ASAR） image, was captured in Dongsha Islands surrounding area on July 22, 2011. Considering the formation mechanism of internal waves, two important issues in the EMD method-the curve fitting and end effects-were studied. After comparing different algorithms, the cubic spline interpolation（CSI） was used for curve fitting and the boundary full-wave（BFW） method was applied to inhibit the end effects. Used this inversion method, the internal wave signal was extracted from the ASAR image, the distance of the internal wave between peak and trough was calculated, and the half-width of soliton was obtained as well. In addition, the inversion result is consistent with the previous experimental findings, which indicates the effectiveness of our algorithm.

A two-level method for sparse time-frequency representation of multiscale data Dedicated to Professor LI TaTsien on the Occasion of His 80th Birthday

Based on the recently developed data-driven time-frequency analysis(Hou and Shi, 2013), we propose a two-level method to look for the sparse time-frequency decomposition of multiscale data. In the two-level method, we first run a local algorithm to get a good approximation of the instantaneous frequency. We then pass this instantaneous frequency to the global algorithm to get an accurate global intrinsic mode function(IMF)and instantaneous frequency. The two-level method alleviates the difficulty of the mode mixing to some extent.We also present a method to reduce the end effects.

A Proposal of a Spline Filter that Achieves Both Robustness and Lower Compatibility

A spline filter is used to extract roughness profiles for the measurement of surface texture and is useful when sufficient sections before and after a primary profile could not be secured.This is because a spline filter could prevent the end effect,which is the fluctuation of output data that occurs around both ends of the primary profile and depends on the width of the weighting function of a filter.The spline filter is based on the calculation of an inverse matrix instead of the convolution of the weighting function of the filters.When input data include outliers,the output of a spline filter greatly fluctuates.To solve this problem,we propose a robust spline filter.However,output of the robust spline is not in agreement with that of the spline filter when input data do not include outliers.Thus,the robust spline filter has no lower compatibility.In this paper,the"Fast M-estimation Spline Filter(FMSF)"is proposed.FMSF uses the fast M-estimation method.FMGF performs robust to input data including outliers,and gives the same output as that of general spline filters to input data without outliers.The value estimated by this method is in agreement with that estimated by the least squares method if no outlier exists.In order to apply the fast M-estimation method to the spline filter,convolution of weight function is used instead of the inverse matrix.And the input geometry with shear and point-symmetric extensions is pre-processed to prevent the end effect.