Measurement of remanent magnetic moment using a torsion pendulum with single frequency modulation method

In Tian Qin spaceborne gravitational-wave detectors, the stringent requirements on the magnetic cleanliness of the test masses demand the high resolution ground-based characterization measurement of their magnetic properties. Here we present a single frequency modulation method based on a torsion pendulum to measure the remanent magnetic moment mr of 1.1 kg dummy copper test mass, and the measurement result is(6.45 ± 0.04(stat) ± 0.07(syst)) × 10^(-8)A · m^(2). The measurement precision of the mr is about 0.9 n A · m^(2), well below the present measurement requirement of Tian Qin. The method is particularly useful for measuring extremely low magnetic properties of the materials for use in the construction of space-borne gravitational wave detection and other precision scientific apparatus.

Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential

Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time （HB-AFT） do- main technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.

Harmonic Balance Methods:A Review and Recent Developments

The harmonic balance(HB)method is one of the most commonly used methods for solving periodic solutions of both weakly and strongly nonlinear dynamical systems.However,it is confined to low-order approximations due to complex symbolic operations.Many variants have been developed to improve the HB method,among which the time domain HB-like methods are regarded as crucial improvements because of their fast computation and simple derivation.So far,there are two problems remaining to be addressed.i)A dozen of different versions of HB-like methods,in frequency domain or time domain or in hybrid,have been developed;unfortunately,misclassification pervades among them due to the unclear borderlines of different methods.ii)The time domain HB-like methods suffer from non-physical solutions,which have been shown to be caused by aliasing(mixture of the high-order into the low-order harmonics).Although a series of dealiasing techniques have been developed over the past two decades,the mechanism of aliasing and the final solution to dealiasing are still not well known to the academic community.This paper aims to provide a comprehensive review of the development of HB-like methods and enunciate their principal differences.In particular,the time domain methods are emphasized with the famous aliasing phenomenon clearly addressed.

Modal Identification of Offshore Platforms Using Statistical Method Based on ERA

Identification of modal parameters of a linear structure with output-only measurements has received much attention over the past decades. In the paper, the Natural Excitation Technique (NExT) is used for acquisition of the impulse signals from the structural responses. Then Eigensystem Realization Algorithm (ERA) is utilized for modal identification. For disregarding the fictitious ‘computational modes', a procedure, Statistically Averaging Modal Frequency Method (SAMFM), is developed to distinguish the true modes from noise modes, and to improve the precision of the identified modal frequencies of the structure. An offshore platform is modeled with the finite element method. The theoretical modal parameters are obtained for a comparison with the identified values. The dynamic responses of the platform under random wave loading are computed for providing the output signals used for identification with ERA. Results of simulation demonstrate that the proposed method can determine the system modal frequency with high precision.

Experimental Investigation on Electromagnetic Attenuation by Low Pressure Radio-Frequency Plasma for Cavity Structure

This paper reports on an experiment designed to test electromagnetic（EM）attenuation by radio-frequency（RF）plasma for cavity structures.A plasma reactor,in the shape of a hollow cylinder,filled with argon gas at low pressure,driven by a RF power source,was produced by wave-transmitting material.The detailed attenuations of EM waves were investigated under different conditions：the incident frequency is 1-4 GHz,the RF power supply is 13.56 MHz and1.6（-3） k W,and the argon pressure is 75-200 Pa.The experimental results indicate that 5-15 d B return loss can be obtained.From a first estimation,the electron density in the experiment is approximately（1.5-2.2）×1016m（-3）and the collision frequency is about 11（-3）0 GHz.The return loss of EM waves was calculated using a finite-difference time-domain（FDTD）method and it was found that it has a similar development with measurement.It can be confirmed that RF plasma is useful in the stealth of cavity structures such as jet-engine inlet.

Frequency Weighting Filter Design for Automotive Ride Comfort Evaluation

Few study gives guidance to design weighting filters according to the frequency weighting factors,and the additional evaluation method of automotive ride comfort is not made good use of in some countries.Based on the regularities of the weighting factors,a method is proposed and the vertical and horizontal weighting filters are developed.The whole frequency range is divided several times into two parts with respective regularity.For each division,a parallel filter constituted by a low-and a high-pass filter with the same cutoff frequency and the quality factor is utilized to achieve section factors.The cascading of these parallel filters obtains entire factors.These filters own a high order.But,low order filters are preferred in some applications.The bilinear transformation method and the least P-norm optimal infinite impulse response（IIR） filter design method are employed to develop low order filters to approximate the weightings in the standard.In addition,with the window method,the linear phase finite impulse response（FIR） filter is designed to keep the signal from distorting and to obtain the staircase weighting.For the same case,the traditional method produces 0.330 7 m · s^–2 weighted root mean square（r.m.s.） acceleration and the filtering method gives 0.311 9 m · s^–2 r.m.s.The fourth order filter for approximation of vertical weighting obtains 0.313 9 m · s^–2 r.m.s.Crest factors of the acceleration signal weighted by the weighting filter and the fourth order filter are 3.002 7 and 3.011 1,respectively.This paper proposes several methods to design frequency weighting filters for automotive ride comfort evaluation,and these developed weighting filters are effective.

Methods to Improve the Long Distance Time-Varying Channel Transmission Performance of Expendable Profiler

To improve the transmission performance of XCTD channel, this paper proposes a method to measure directly and fit the channel transmission characteristics by using frequency sweeping method. Sinusoidal signals with a frequency range of 100 Hz to 10 k Hz and an interval of 100 Hz are used to measure transmission characteristics of channels with lengths of 300 m, 800 m, 1300 m, and 1800 m. The correctness of the fitted channel characteristics by transmitting square wave, composite waves of different frequencies, and ASK modulation are verified. The results show that when the frequency of the signal is below 1500 Hz, the channel has very little effect on the signal. The signal compensated for amplitude and phase at the receiver is not as good as the uncompensated signal.Alternatively, when the signal frequency is above 1500 Hz, the channel distorts the signal. The quality of signal compensated for amplitude and phase at receiver is better than that of the uncompensated signal. Thus, we can select the appropriate frequency for XCTD system and the appropriate way to process the received signals. Signals below1500 Hz can be directly used at the receiving end. Signals above 1500 Hz are used after amplitude and phase compensation at the receiving end.

A Data Transmission Method Using a Cyclic Redundancy Check and Inaudible Frequencies

This paper describes a data transmission method using a cyclic redundancy check and inaudible frequencies.The proposed method uses inaudible high frequencies from 18 k Hz to 22 k Hz generated via the inner speaker of smart devices.Using the proposed method,the performance is evaluated by conducting data transmission tests between a smart book and smart phone.The test results confirm that the proposed method can send 32 bits of data in an average of 235 ms,the transmission success rate reaches 99.47%,and the error detection rate of the cyclic redundancy check is0.53%.

Diagnosis of Disc Space Variation Fault Degree of Transformer Winding Based on K-Nearest Neighbor Algorithm

Winding is one of themost important components in power transformers.Ensuring the health state of the winding is of great importance to the stable operation of the power system.To efficiently and accurately diagnose the disc space variation(DSV)fault degree of transformer winding,this paper presents a diagnostic method of winding fault based on the K-Nearest Neighbor(KNN)algorithmand the frequency response analysis(FRA)method.First,a laboratory winding model is used,and DSV faults with four different degrees are achieved by changing disc space of the discs in the winding.Then,a series of FRA tests are conducted to obtain the FRA results and set up the FRA dataset.Second,ten different numerical indices are utilized to obtain features of FRA curves of faulted winding.Third,the 10-fold cross-validation method is employed to determine the optimal k-value of KNN.In addition,to improve the accuracy of the KNN model,a comparative analysis is made between the accuracy of the KNN algorithm and k-value under four distance functions.After getting the most appropriate distance metric and kvalue,the fault classificationmodel based on theKNN and FRA is constructed and it is used to classify the degrees of DSV faults.The identification accuracy rate of the proposed model is up to 98.30%.Finally,the performance of the model is presented by comparing with the support vector machine(SVM),SVM optimized by the particle swarmoptimization(PSO-SVM)method,and randomforest(RF).The results show that the diagnosis accuracy of the proposed model is the highest and the model can be used to accurately diagnose the DSV fault degrees of the winding.

A flextensional transducer and its algorithmic method of resonant frequency

A flextensional transducer with an Omega shape and its algorithmic method of the resonant frequency and the shape functions are suggested. The Omega transducer is separated into four parts treated respectively as a thin shell of revolution and the theories of thin shells of revolution and piezoelectricity are used to obtain the energy functional of each part so that the sum of the energy functionals of the four parts is the energy functional of the whole Omega transducer. By substituting the shape functions with undetermined coefi3cients and the geo- metrical boundary conditions into the energy functional of the Omega transducer, the resonant frequency of the Omega transducer is firstly determined with the Rayleigh-Ritz method. With the gotten resonant frequency, the constant coefficients of the shape functions are following solved through the Rayleigh-Ritz partial differential equations and the geometrical boundary condition equations. The solving method of the resonant frequency and the shape functions is also extended to the cymbal transducer. Such an analytical method is verified to be feasible by the results of the finite element analysis and experiments. The research indicates that （1） The radial vibration of the piezoelectric ceramic is in phase with the longitudinal vibration of the top of metal cap, and it cut down the reversed phase component in the sound field. The Omega transducer can be a low frequency transducer. （2） The determination method of the resonant frequency and the shape functions give a solution to the optimum designs of the Omega transducer and the cymbal transducer. （3） The determination method of the resonant fi＇equency and the shape functions can also be used in other flextensional transducers or other structures which are composed of thin shells of revolution, so it is universal.

Low frequency ultrasonic multi-mode Lamb wave method for characterizing the ultra-thin transversely isotropic laminate composite: Theory and experiment

A low-frequency multi-mode ultrasonic Lamb wave method suitable for character- izing the thickness, the density and the elastic constants of the ultra-thin transversely isotropic laminate composite is presented. The 'ultra-thin' here means that the thickness of the plate is much less than the wavelength of the ultrasonic wave so that the echoes from the front and back faces of the plate can't be separated in the time domain. The dispersion equations for the low frequency ultrasonic Lamb waves with the propagation directions parallel and vertical to the fiber direction are derived. In conjunction with the least square algorithm method, the secant algorithm is used to estimate the parameters of the ultra-thin fiber-reinforced composite layer. The evaluation errors and the sensitivity of the method to different paramters of the thin composite are analyzed. The technique has been used to characterize the ultra-thin grass fiber reinforced PES composite with thickness down to ten percents of the ultrasonic wavelength. It is observed that the agreement between the nominal and the estimation values is reasonably good.

GLOBAL EXISTENCE AND L^p ESTIMATES FOR SOLUTIONS OF DAMPED WAVE EQUATION WITH NONLINEAR CONVECTION IN MULTI-DIMENSIONAL SPACE

In this article, the author studies the Cauchy problem of the damped wave equation with a nonlinear convection term in multi-dimensions. The author shows that a classical solution to the Cauchy problem exists globally in time under smallness condition on the initial perturbation. Furthermore, the author obtains the L^p （2 ≤ p ≤ ∞） decay estimates of the solution.

Stability analysis of the simplest Takagi-Sugeno fuzzy control system using circle criterion

A frequency-domain-based sufficient condition is derived to guarantee the globally asymptotic stability of the simplest Takagi-Sugeno （T-S） fuzzy control system by using the circle criterion. The analysis is performed in the frequency domain, and hence the condition is of great significance when the frequency-response method, which is widely used in the linear control theory and practice, is employed to synthesize the simplest T-S fuzzy controller. Besides, this sufficient condition is featured by a graphical interpretation, which makes the condition straightforward to be used. Comparisons are drawn between the performance of the simplest T-S fuzzy controller and that of the linear compensator. Two numerical examples are presented to demonstrate how this sufficient condition can be applied to both stable and unstable plants.

Ultra low frequeney electromagnetic wave anomaly and its spectrum characteristics before earthquakes

Many observations and researches show that abundant and intense ultra low frequency (ULF) electromagneticanomalies appears before local earthquakes. In order to understand this phenomenon systematically, the trans-mission property and the formation of the seismic-electric dipole are discussed in this paper. The results showthat the vertical component Of the ULF electric anomaly before earthquake has the properties of better penetration, less disturbance and high signal-to-noise ratio. The signal can be easily extracted and received. The anomaly should be an important way to seek for reliable short-term and imminent earthquake precursors. After thespectrum analysis of the (ULF) electric field anomalies, we found that the periods of the anomaly related to localearthquakes are from a few minutes to a dozens minutes. There is a relation between the spectrum of the anomaly and the epicentral distance. The ULF electric field anomalies strongly rely on the orientation of the seismo-genie zone. The percolation electric field anomaly and its spectrum amplitude do not have obvious relation withthe size of local earthquakes.

Investigation of Rotor Radial Rotating Error upon AMB System

This paper first suggests the use of the Fourier frequency transmission method of two dimensions function （ 2D FFT） to analyze radial rotating errors that occurred in a rotor. Based on this method a magnetic rotor is measured. The authors point out that the main cause to affect radial rotating accuracy of the rotating shaft at a high speed is the dynamic imbalance of the shaft itself. Finally the feedforward control scheme is suggested to improve the accuracy of the shaft in an active magnetic bearing （ AMB ） system.

Study of Unforced Unsteadiness in Centrifugal Pump at Partial Flow Rates

In order to explore the unforced unsteadiness of centrifugal pumps,a 2-D frequency domain imaging display technology was used to study the development of these unsteady flow structures at partial flow conditions.The results showed that,the unsteady flow field was not only affected by rotor and stator interaction,but also appeared an unforced unsteadiness with fundamental frequency of St≈0.23 around the impeller throat area.Moreover,as the flow rates decreased,this unsteady flow structure gradually weakened and disappeared.When the flow rate was reduced to 0.6 times of design flow rate,another two unforced unsteady flow structures with characteristic frequencies of St≈0.0714 and St≈0.12 began to appear in the same area.Therefore,with the operating condition smaller than design flow rate,the internal flow became more and more complex.In addition to the forced unsteadiness,the unforced unsteadiness which is not connected with the blade passage frequency became more and more obvious.

Retard function and ship motions with forward speed in time-domain

The time-domain calculations of retard function and ship motions in waves by the direct time-domain method （DTM） and the frequency to time-domain transformation method （FTTM） are compared and analyzed. A Wigley-hull-form ship and an $60 ship moving in waves are examined, and the corresponding retard functions are in good agreement with those given by DTM and FTTM. The comparison of retard functions in different forward speeds by the two methods is observed, and the results of ship motions in forward speed are also compared with the experimental data. On this basis, the advantage and disadvantage of them are discussed.

Energy Decay of Solutions to a Nondegenerate Wave Equation with a Fractional Boundary Control

In this paper,we study the energy decay rate for a one-dimensional nondegenerate wave equation under a fractional control applied at the boundary.We proved the polynomial decay result with an estimation of the decay rates.Our result is established using the frequency-domain method and Borichev-Tomilov theorem.

Real-Time MRI-Controlled Ultrasound Hyperthermia System for Superficial Tumor Treatment

Ultrasound hyperthermia is one of the most important methods in tumor treatment and characterized by non-invasiveness. Magnetic resonance imaging(MRI)-based temperature mapping techniques are safe compared with invasive methods and have been applied to detect temperature changes for a variety of applications. Among these techniques, the proton resonance frequency(PRF) method is relatively advanced. With a temperature measuring experiment, the effectiveness of PRF method has been proved, because the outcome temperature curve and the real temperature curve fit well. After that, an experiment has been conducted on tumors inside rabbit legs and the result indicates that this system is able to performance hyperthermia at targets based on PRF method in temperature mapping.

Change of bio-electric interferential currents of acute fatigue and recovery in male sprinters

We studied the muscle fatigue and recovery of thirty male sprinters(aged 18–22 years)using the Frequency Analysis Method(FAM).The interferential currents(ICs)with different thresholds for sensory,motor and pain responses,the maximal voluntary contraction(MVC),and the amplitude of the surface EMG(aEMG,sEMG)were assessed prior to and immediately after an acute explosive fatigue training session,and during one-week recovery.We found that IC increased on average from 32.38.9 mA to 37.57.5 mA in sensory response at 10 Hz immediately post training(p=0.004)but decreased at 24-hr post training(p=0.008)and returned to pre-levels thereafter.Motor and pain response patterns at 10 Hz were similar(motor:p=0.033 and 0.040;pain:p=0.022 and 0.019,respectively).The change patterns of ICs were similar to but prior to the changes of sEMG.The agreement between IC assessment and amplitude of sEMG(aEMG)/MVC ratio was good(>95%).The present study suggested that the changes in ICs were prior to the changes in both the aEMG and force during fatigue.These changes may reflect the physiological sensory change due to peripheral fatigue.FAM may be useful as an effective early detection and simple tool for monitoring muscle fatigue during training and recovery in athletes.