Power spectral density analysis for nonlinear systems based on Volterra series

A consequence of nonlinearities is a multi-harmonic response via a monoharmonic excitation.A similar phenomenon also exists in random vibration.The power spectral density(PSD)analysis of random vibration for nonlinear systems is studied in this paper.The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function(GFRF).For a class of nonlinear systems,the growing exponential method is used to determine the first 3 rd-order GFRFs.The proposed approach is used to achieve the nonlinear system’s output PSD under a narrow-band stationary random input.The relationship between the peak of PSD and the parameters of the nonlinear system is discussed.By using the proposed method,the nonlinear characteristics of multi-band output via single-band input can be well predicted.The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system’s output PSD.This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.

Modeling of Noise Power Spectral Density Analysis for GaN/AlGaN HEMT

Nano Technology is the branch of technology that deals with dimensions and tolerances in terms of nanometers. In this paper, the electrical characteristics analysis is determined for the Nano-GaN HEMT and Micro-GaN HEMT and also power spectrum density is determined for GaN Nano-HEMT by reducing the gate length Lg in nm range. The GaN Nano HEMT is producing high current comparing to Micro GaN HEMT. Accuracy of the proposed analytical model results is verified with simulation results.

A new spatial coherence model and analytical coeffi cients for multi-support response spectrum combination

In this paper, a new spatial coherence model of seismic ground motions is proposed by a fitting procedure. The analytical expressions of modal combination （correlation） coefficients of structural response are developed for multi-support seismic excitations. The coefficients from both the numerical integration and analytical solutions are compared to verify the accuracy of the solutions. It is shown that the analytical expressions of numerical modal combination coefficients are of high accuracy. The results of random responses of an example bridge show that the analytical modal combination coefficients developed in this paper are accurate enough to meet the requirements needed in practice. In addition, the computational efficiency of the analytical solutions of the modal combination coefficients is demonstrated by the response computation of the example bridge. It is found that the time required for the structural response analysis by using the analytical modal combination coefficients is less than 1/20 of that using numerical integral methods.

Bispectrum Feature Extraction of Gearbox Faults Based on Nonnegative Tucker3 Decomposition with 3D Calculations

Nonnegative Tucker3 decomposition（NTD） has attracted lots of attentions for its good performance in 3D data array analysis. However, further research is still necessary to solve the problems of overfitting and slow convergence under the anharmonic vibration circumstance occurred in the field of mechanical fault diagnosis. To decompose a large-scale tensor and extract available bispectrum feature, a method of conjugating Choi-Williams kernel function with Gauss-Newton Cartesian product based on nonnegative Tucker3 decomposition（NTD_EDF） is investigated. The complexity of the proposed method is reduced from o（nNlgn） in 3D spaces to o（RiR2nlgn） in 1D vectors due to its low rank form of the Tucker-product convolution. Meanwhile, a simultaneously updating algorithm is given to overcome the overfitting, slow convergence and low efficiency existing in the conventional one-by-one updating algorithm. Furthermore, the technique of spectral phase analysis for quadratic coupling estimation is used to explain the feature spectrum extracted from the gearbox fault data by the proposed method in detail. The simulated and experimental results show that the sparser and more inerratic feature distribution of basis images can be obtained with core tensor by the NTD EDF method compared with the one by the other methods in bispectrum feature extraction, and a legible fault expression can also be performed by power spectral density（PSD） function. Besides, the deviations of successive relative error（DSRE） of NTD_EDF achieves 81.66 dB against 15.17 dB by beta-divergences based on NTD（NTD_Beta） and the time-cost of NTD EDF is only 129.3 s, which is far less than 1 747.9 s by hierarchical alternative least square based on NTD （NTD_HALS）. The NTD_EDF method proposed not only avoids the data overfitting and improves the computation efficiency but also can be used to extract more inerratic and sparser bispectrum features of the gearbox fault.

Analysis of vibration and frequency transmission of high speed EMU with flexible model

When the operation speed of the high-speed train increases and the weight of the carbody becomes lighter,not only does the sensitivity of the wheel/rail contact get higher,but also the vibration frequency range of the vehicle system gets enlarged and more frequencies are transmitted from the wheelset to the carbody.It is important to investigate the vibration characteristics and the dynamic frequency transmission from the wheel/rail interface to the carbody of the high-speed electric multi-uint（EMU）.An elastic highspeed vehicle dynamics model is established in which the carbody,bogieframes,and wheelsets are all dealt with as flexible body.A rigid high-speed vehicle dynamics model is set up to compare with the simulation results of the elastic model.In the rigid vehicle model,the carbody,bogieframes and wheelsets are treated as rigid component while the suspension and structure parameters are the same as used in the elastic model.The dynamic characteristic of the elastic high speed vehicle is investigated in time and frequency domains and the di ff erence of the acceleration,frequency distribution and transmission of the two types of models are presented.The results show that the spectrum power density of the vehicle decreases from the wheelset to the carbody and the acceleration transmission ratio is approximately from 1%to 10%for each suspension system.The frequency of the wheelset rotation is evident in the vibration of the flexible model and is transmitted from the wheelset to the bogieframe and to thecarbody.The results of the flexible model are more reasonable than that of the rigid model.A field test data of the high speed train are presented to verify the simulation results.It shows that the simulation results are coincident with the field test data.

Mechanism of micro-waviness induced KH_2PO_4 crystal laser damage and the corresponding vibration source

The low laser induced damage threshold of the KH2PO4 crystal seriously restricts the output power of inertial confinement fusion.The micro-waviness on the KH2PO4 surface processed by single point diamond turning has a significant influence on the damage threshold.In this paper,the influence of micro-waviness on the damage threshold of the KH2PO4 crystal and the chief sources introducing the micro-waviness are analysed based on the combination of the Fourier modal theory and the power spectrum density method.Research results indicate that among the sub-wavinesses with different characteristic spatial frequencies there exists the most dangerous frequency which greatly reduces the damage threshold,although it may not occupy the largest proportion in the original surface.The experimental damage threshold is basically consistent with the theoretical calculation.For the processing parameters used,the leading frequency of micro-waviness which causes the damage threshold to decrease is between 350-1 μm-1 and 30-1 μm-1,especially between 90-1 μm-1 and 200-1 μm-1.Based on the classification study of the time frequencies of microwaviness,we find that the axial vibration of the spindle is the chief source introducing the micro-waviness,nearly all the leading frequencies are related to the practical spindle frequency（about 6.68 Hz,400 r/min） and a special middle frequency（between 1.029 Hz and 1.143 Hz）.

Parametric characteristic of the random vibration response of nonlinear systems

Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.

Dynamic modeling of ultra-precision fly cutting machine tool and the effect of ambient vibration on its tool tip response

The dynamic performances of an ultra-precision fly cutting machine tool(UFCMT)has a dramatic impact on the quality of ultra-precision machining.In this study,the dynamic model of an UFCMT was established based on the transfer matrix method for multibody systems.In particular,the large-span scale flow field mesh model was created;and the variation in linear and angular stiffness of journal and thrust bearings with respect to film thickness was investigated by adopting the dynamic mesh technique.The dynamic model was proven to be valid by comparing the dynamic characteristics of the machine tool obtained by numerical simulation with the experimental results.In addition,the power spectrum density estimation method was adopted to simulate the statistical ambient vibration excitation by processing the ambient vibration signal measured over a long period of time.Applying it to the dynamic model,the dynamic response of the tool tip under ambient vibration was investigated.The results elucidated that the tool tip response was significantly affected by ambient vibration,and the isolation foundation had a good effect on vibration isolation.

Resonant behavior of stochastic oscillations of general relativistic disks driven by a memory-damped friction

By using a generalized Langevin equation to describe the vertieal oscillations of a general relativistic disk subjected to a memory-damped friction and a stochastic force, we derive the power spectrum density （PSD） of accretion disk oscillating luminosity by the method of Laplace transform, and discuss the influence of the system parameters on the resonant behavior in PSD curves. The results show that as the damping strength a and memory time τ of the friction increase, the variation of PSD with spectrum frequency f from monotonous decreasing to occurring maximums, and the phenomenon of a general stochastic resonance （SR） with a single peak and multi-peaks can be found in PSD curves. The radial distance parameter n, the mass M, and spin parameter a, of the black hole determine the inherent frequency of vertical oscillations in the disk, and they have significant influences on the SR phenomena in a system of black hole binaries.

Extraction and verification of coherent structures in near-wall turbulence

According to the characteristics of coherent structures in near-wall turbulence, an accurate extraction and verification method is developed based on wavelet transform （WT） and correlation analysis in this paper. At first, the fluid field of a turbulent boundary layer is measured precisely in a gravitational low-speed water tunnel. On the basis of the distribution of the coherent structures, velocity data of three test points are selected and analyzed, whose dimensionless heights are 20.8, 33.5, and 42.6. According to the frequency range of power spectrum density （PSD）, coherent and incoherent structures are both extracted from the original signals using continuous and orthogonal wavelet transforms. To confirm the validity of the extracted signals, the probability density function （PDF） of each extracted signal is calculated. The result demonstrates that the incoherent structures obey the Gaussian distribution, while the coherent structures deviate from the Gaussian distribution. The PDFs of the coherent structures and the original signals are similar, which shows that the coherent structures make most contributions to the turbulence. For further verification, a correlation parameter between coherent and incoherent structures is defined, which evidently proves the validity of the extraction method in this paper.

Analysis and Algorithm Simulation of Forward-link CDMA Signal Spectral Regrowth

Closed-form expressions for the spectral regrowth of CDMA signal passing through a nonlinear amplifier with a digitally modulated carrier are derived using the power series and statistical methods of high-order cumulant. The technique yields an analytical expression for the autocorrelation function of the output signal as a function of the statistics of the input signal transformed by a behavioral model of the amplifier. The third-order nonlinearity is expressed in terms of IP3 to include the memory effects of the circuit in-band and out-of-band reactance. The analysis is based on a time-domain model of the signal and the model is used to derive the power spectrum density and other statistical properties of the CDMA signal. Such analytical results are useful in finding optimal operating conditions of the power Amplifier.

Electron densitymap evaluation functions for determining the quality of protein crystal structures

Background Finding methods to judge the quality of X-ray crystallographic information is an active research topic.The quality of electron density maps reconstructed by Fourier transform is always limited by the finite resolution,the amplitude/phase error and the completeness of diffraction data.At present,the R value and effective resolution are common ways of evaluating the quality of electron density maps.Unfortunately,the current evaluation methods are only dependent on diffraction amplitude,without any phase information.Methods Advanced evaluation functions in real space are designed to estimate the electron density map quality.The electron density map definition evaluation function relies on the atomicity of the electron density distribution.We use the power spectrum electron density entropy in protein crystallography for the first time.These two functions include both structure factor amplitudes and phases via the Fourier transform of electron density map.Results We carry out tests on synthetic data sets of known structures,varying the resolution and error,and draw the quality curves of electron density maps with theoretical,noisy and experimental diffraction data by two evaluation functions at different resolutions.The curves reveal the optimum structure and resolution of proteins clearly.Conclusions The work presented here offers new methods to evaluate the qualities of the electron density maps of proteins with slight differences,and brand new indicators to select the optimum diffraction resolution of protein structures.

Short-term prediction of influent flow rate and ammonia concentration in municipal wastewater treatment plants

The prediction of the influent load is of great importance for the improvement of the control system to a large wastewater treatment plant. A systematic data analysis method is presented in this paper in order to estimate and predict the periodicity of the influent flow rate and ammonia （NH3） concentrations： 1） data filtering using wavelet decomposition and reconstruction; 2） typical cycle identification using power spectrum density analysis; 3） fitting and prediction model establishment based on an autoregressive model. To give meaningful information for feedforward control systems, predictions in different time scales are tested to compare the corresponding predicting accuracy. Considering the influence of the rainfalls, a linear fitting model is derived to estimate the relationship between flow rate trend and rain events. Measurements used to support coefficient fitting and model testing are acquired from two municipal wastewater treatment plants in China. The results show that 1） for both of the two plants, the periodicity affects the flow rate and NH3 concentrations in different cycles （especially cycles longer than 1 day）; 2） when the flow rate and NH3 concentrations present an obvious periodicity, the decreasing of prediction accuracy is not distinct with increasing of the prediction time scales; 3） the periodicity influence is larger than rainfalls; 4） the rainfalls will make the periodicity of flow rate less obvious in intensive rainy periods.

Estimation method for random sonic fatigue life of thin-walled structure of a combustor liner based on stress probability distribution

As to the sonic fatigue problem of an aero-engine combustor liner structure under the random acoustic loadings,an effective method for predicting the fatigue life of a structure under random loadings was studied.Firstly,the probability distribution of Von Mises stress of thin-walled structure under random loadings was studied,analysis suggested that probability density function of Von Mises stress process accord approximately with two-parameter Weibull distribution.The formula for calculating Weibull parameters were given.Based on the Miner linear theory,the method for predicting the random sonic fatigue life based on the stress probability density was developed,and the model for fatigue life prediction was constructed.As an example,an aero-engine combustor liner structure was considered.The power spectrum density(PSD) of the vibrational stress response was calculated by using the coupled FEM/BEM(finite element method/boundary element method) model,the fatigue life was estimated by using the constructed model.And considering the influence of the wide frequency band,the calculated results were modified.Comparetive analysis shows that the estimated results of sonic fatigue of the combustor liner structure by using Weibull distribution of Von Mises stress are more conservative than using Dirlik distribution to some extend.The results show that the methods presented in this paper are practical for the random fatigue life analysis of the aeronautical thin-walled structures.

6°攻角圆锥边界层中的高频不稳定性实验研究

本文在马赫6静风洞中对6◦攻角圆锥边界层中的高频不稳定性进行了研究,实验的单位雷诺数是6:90×10^(6)m^(−1).使用Kulite和PCB脉动压力传感器测量了圆锥壁面的高频脉动压力信号,并使用基于纳米示踪的平面激光散射(NPLS)技术对三维边界层中的相干结构进行测量.结果表明,在圆锥背风面存在低频和高频的扰动波信号,特征频率分别为10-20 kHz和120-140 kHz.由NPLS结果可知,低频信号对应行进横流波结构,高频信号位于行进横流波结构的顶部,为行进横流波的二次不稳定性.另外,使用PCB传感器阵列对高频不稳定性的频率和幅值增长特性进行了研究,得到了高频不稳定性的幅值增长云图.

Application of CFD-DEM to the study of solid exchange in a dual-leg fluidized bed

The CFD-DEM model was developed to simulate solid exchange behavior between two half beds in a bench-scale two-dimensional dual-leg fluidized bed （DL-FB）. Power spectrum density （PSD） analysis was applied to obtain the dominant frequency （F） of the simulated differential particle number （APLR） between the two half beds. Effects of fluidization velocity （u） and bed material inventory （H） on the solid exchange behavior were studied using the CFD-DEM model. Not only snapshots of the simulated particle flow patterns using the OpenGL code but also the dominant frequency of APLR was similar to the experimental results. The simulation results show that higher fluidization velocity assists the exchange of more particles between the two half beds, but the dispersion of clusters on the bed surface into single particles decreases the cluster exchange frequency. A greater bed material inventory results in more intense cluster exchange. The cluster exchange frequency decreases with an increase of the bed material inventory.