Weighted Multi-sensor Data Level Fusion Method of Vibration Signal Based on Correlation Function

As the differences of sensor＇s precision and some random factors are difficult to control,the actual measurement signals are far from the target signals that affect the reliability and precision of rotating machinery fault diagnosis.The traditional signal processing methods,such as classical inference and weighted averaging algorithm usually lack dynamic adaptability that is easy for trends to cause the faults to be misjudged or left out.To enhance the measuring veracity and precision of vibration signal in rotary machine multi-sensor vibration signal fault diagnosis,a novel data level fusion approach is presented on the basis of correlation function analysis to fast determine the weighted value of multi-sensor vibration signals.The approach doesn＇t require knowing the prior information about sensors,and the weighted value of sensors can be confirmed depending on the correlation measure of real-time data tested in the data level fusion process.It gives greater weighted value to the greater correlation measure of sensor signals,and vice versa.The approach can effectively suppress large errors and even can still fuse data in the case of sensor failures because it takes full advantage of sensor＇s own-information to determine the weighted value.Moreover,it has good performance of anti-jamming due to the correlation measures between noise and effective signals are usually small.Through the simulation of typical signal collected from multi-sensors,the comparative analysis of dynamic adaptability and fault tolerance between the proposed approach and traditional weighted averaging approach is taken.Finally,the rotor dynamics and integrated fault simulator is taken as an example to verify the feasibility and advantages of the proposed approach,it is shown that the multi-sensor data level fusion based on correlation function weighted approach is better than the traditional weighted average approach with respect to fusion precision and dynamic adaptability.Meantime,the approach is adaptable and easy to use,can be applied to other areas of vibration measurement.

MODAL PARAMETERS EXTRACTION WITH CROSS CORRELATION FUNCTION AND CROSS POWER SPECTRUM UNDER UNKNOWN EXCITATION

In most of real operational conditions only response data are measurable while the actual excitations are unknown, so modal parameter must be extracted only from responses. This paper gives a theoretical formulation for the cross correlation functions and cross power spectra between the outputs under the assumption of white noise excitation. It widens the field of modal analysis under ambient excitation because many classical methods by impulse response functions or frequency response functions can be used easily for modal analysis under unknown excitation. The Polyreference Complex Exponential method and Eigensystem Realization Algorithm using cross correlation functions in time domain and Orthogonal Polynomial method using cross power spectra in frequency domain are applied to a steel frame to extract modal parameters under operational conditions. The modal properties of the steel frame from these three methods are compared with those from frequency response functions analysis. The results show that the modal analysis method using cross correlation functions or cross power spectra presented in this paper can extract modal parameters efficiently under unknown excitation.

Temporal variation of noise correlation function(NCF) in Beijing and surroundings:Its relation with climate events and implications

Noise correlation function （NCF） was calculated using the data of the Beijing Capital-Area Telemetered Digital Seismograph Network from June 12 to September 12, 2005. Signal-to-noise ratio （SNR） is used to characterize the quality of NCF at each station pair. The SNR （in dB） is shown to be dependent on the separation distance R of the station pair via SNR= A -BlogR. ＇Normalized average SNR＇ for all the station pairs can then be calculated, as represented by the value of SNR taking R = 250 km in the empirical SNR-R relation, to measure the overall quality of the NCF result. The ＇normalized average SNR＇ of the NCF shows temporal variation and is apparently dependent on the root-mean-square （RMS） velocity of the microseism. The result obtained by this experiment provides clues to the explanation of the properties of NCF, such as the dominant mechanism underlying （diffuse wave fields or uncorrelated sources）, and the dependence of SNR on the time length of recordings.

Spin-correlation function of the fully frustrated Ising model and ±J Ising spin glass on a square lattice

In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as the correlation function. We estimate the exponent of spin correlation function for the fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.

Dynamical correlation functions of the quadratic coupling spin-Boson model

The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method.We focus on the dynamical auto-correlation functions CO（ω）, with the operator taken as σx, σz, and X, respectively. In the weak-coupling regime α 〈 αc, these functions show power law ω-dependence in the small frequency limit, with the powers 1 ＋ 2s, 1 ＋ 2s, and s, respectively. At the critical point α = αc of the boson-unstable quantum phase transition, the critical exponents yO of these correlation functions are obtained as yσx= yσz= 1-2s and yX=-s, respectively. Here s is the bath index and X is the boson displacement operator. Close to the spin flip point, the high frequency peak of Cσx（ω） is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point.

Simulation study of the effects of time delay on the correlation function of a bistable system with correlated noises

The effects of time delay on the fluctuation properties of a bistable system are investigated by simulating its normalised correlation function C（s）. Three cases including linear delay, cubic delay and global delay in the system are considered respectively. The simulation results indicate that the linear delay enhances the fluctuation of the system （reduces the stability of the system） while the cubic delay and global delay weaken it （enforce the stability of the system）, and the effect of cubic delay is more pronounced than the linear delay and global delay.

Simulation study of the two-time intensity correlation function of a two-mode laser system with both pump and quantum noises

This paper investigates the two-time intensity correlation function of a two-mode ring laser system subjected to both pump and quantum noises by stochastic simulation. It finds that the decay rate of the intensity correlation function of one mode gets faster with decreasing values of relevant parameters, i.e., the coupling constant ξ, the cross-correlation coefficient A, the difference of the pump parameters Aa and the pump parameter al; however, its variations get complex in the other mode when relevant parameters are changed. The investigating results also show that the effects of the mode competition on intensity correlation function are obvious.

Second-Order Correlation Function for Asymmetric-to-Symmetric Transitions due to Spectrally Indistinguishable Biexciton Cascade Emission

We report the observed photon bunching statistics of biexciton cascade emission at zero time delay in single quantum dots by second-order correlation function g（2） （T） measurements under continuous wave excitation. It is found that the bunching phenomenon is independent of the biexciton binding energy when it varies from 0.59 meV to nearly zero. The photon bunching takes place when the exeiton photon is not spectrally distinguishable from the biexciton photon, and either of them can trigger the %tart＇ in a Hanbury-Brown and Twiss setup. However, if the exciton energy is spectrally distinguishable from the biexciton, the photon statistics will become asymmetric and a cross-bunching lineshape can be obtained. The theoretical calculations based on a model of three-level rate-equation analysis are consistent with the result of g（2）（τ） correlation function measurements.

Exchange-Correlation Functional Comparison of Electronic Energies in Atoms Using a Grid Basis

Calculation of total energies of the electronic ground states of atoms forms the basis for the frozen-core pseudopotentials used in atomistic calculations of much larger scale. Reference values for these energies provide a benchmark for the validation of new software to calculate such potentials. In addition, basic atomic-scale electronic properties such as the (first) ionization energy provide a simple check on the approximation used in the calculation method. We present a comparison of the total energies and ionization energies of atoms Z = 1 - 92 calculated in density functional theory with several levels of exchange-correlation functional and the Hartree-Fock method, comparing ionization energies to experiment. We also investigate the role of relativistic treatment on these energies.

Correlation function and the inverse problem in the BD interaction

We study the correlation functions of the B0D+,B+D0 system,which develops a bound state of approximately 40MeV,using inputs consistent with the Tcc(3875)state.Then,we address the inverse problem starting from these correlation functions to determine the scattering observables related to the system,including the existence of the bound state and its molecular nature.The important output of the approach is the uncertainty with which these observables can be obtained,considering errors in the B0D+,B+D0 correlation functions typical of current values in correlation functions.We find that it is possible to obtain scattering lengths and effective ranges with relatively high precision and the existence of a bound state.Although the pole position is obtained with errors of the order of 50%of the binding energy,the molecular probability of the state is obtained with a very small error of the order of 6%.All these findings serve as motivation to perform such measurements in future runs of high energy hadron collisions.

Mathematical modelling of ball and plate system with experimental and correlation function-based model validation

The ball and plate system is an inherently nonlinear under actuated benchmark system used for validating the performance of various control schemes. A mathematical model depicting the dynamics close to that of the system is very much required for such a test bed. In this correspondence, the complete nonlinear model, a simplified nonlinear model, and a linearized model of the ball and plate system are developed. The system comprises a ball and plate mechanism and a rotary servo unit. The ball and plate mechanism is modelled using the Euler–Lagrange method, whereas the rotary servo subsystem is modelled from the first principles. The nonlinear model of the combined system is developed by including the dynamics of the servo motor with gear and rolling resistance between the ball and the plate. The simplified nonlinear model of the system is obtained with suitable assumptions. The model is linearized around the operating point using the Jacobian. The validity of the developed models is investigated through correlation function analysis. The open-loop response of the three models, viz., nonlinear, simplified nonlinear, and linearized models, is analyzed in the MATLAB/Simulink platform. Since the open-loop system is unstable, the experimental validation of the model is performed with a double-loop PSO (particle swarm optimization) PID control scheme.

Genus two correlation functions in CFTs with TT deformation

Since the definition of TT deformation in the curved Riemann surface is obstructive in the literature,we propose a way to do the deformation in the genus two Riemann surfaces by sewing prescription.We construct the correlation functions of conformal field theories(CFTs)on genus two Riemann surfaces with the TT deformation in terms of the perturbative CFT approach.Thanks to sewing construction to form higher genus Riemann surfaces from lower genus ones and conformal symmetry,we systematically obtain the first-order TT correction to the genus two correlation functions in the TT deformed CFTs,e.g.,partition function and one/higher-point correlation functions.

Strangeness S=-2 baryon-baryon interactions and femtoscopic correlation functions in covariant chiral effective field theory

We study the baryon-baryon interactions with strangeness S=-2 and corresponding momentum correlation functions in leading order covariant chiral effective field theory.The relevant low energy constants are determined by fitting to the latest HAL QCD simulations,taking into account all the coupled channels.Extrapolating the so-obtained strong interactions to the physical point and considering both quantum statistical effects and the Coulomb interaction,we calculate the ΛΛ and Ξ^(-)p correlation functions with a spherical Gaussian source and compare them with recent experimental data.We find a good agreement between our predictions and the experimental measurements by using the source radius determined in proton-proton correlations,which demonstrates the consistency between theory,experiment,and lattice QCD simulations.Moreover,we predict the Σ^(+)Σ^(+),Σ^(+)Λ,and Σ^(+)Σ^(-) interactions and corresponding momentum correlation functions.We further investigate the influence of the source shape and size of the hadron pair on the correlation functions studied and show that the current data are not very sensitive to the source shape.Future experimental measurements of the predicted momentum correlation functions will provide a non-trivial test of not only SU(3) flavor symmetry and its breaking but also the baryon-baryon interactions derived in covariant chiral effective field theory.

Source function extracted from single-event HBT correlation functions of hydrodynamical sources

We investigate the single-event two-pion correlation functions for the hydrodynamic particle-emitting sources with the fluctuating initial conditions generated by the Heavy Ion Jet Interaction Generator （HIJING）. Using a three-dimension fast Fourier transform （FFT）, we further extract the source functions from the single-event correlation functions. It is found that the inhomogeneity of the hydrodynamic sources with the fluctuating initial conditions lead to event-by-event fluctuations of the correlation functions and source functions.

Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas

The Lieb-Liniger model is a prototypical integrable model and has been turned into the benchmark physics in theoretical and numerical investigations of low-dimensional quantum systems. In this note, we present various methods for calculating local and nonlocal M-particle correlation functions, momentum distribution, and static structure factor. In particular, using the Bethe ansatz wave function of the strong coupling Lieb-Liniger model, we analytically calculate the two-point correlation function, the large moment tail of the momentum distribution, and the static structure factor of the model in terms of the fractional statistical parameter a = 1 - 2/γ, where γ, is the dimensionless interaction strength. We also discuss the Tan＇s adiabatic relation and other universal relations for the strongly repulsive Lieb-Liniger model in terms of the fractional statistical parameter.

Correlation Functions, Universal Ratios and Goldstone Mode Singularities in n-Vector Models

Correlation functions in the O(n)models below the critical temperature are considered.Based on Monte Carlo(MC)data,we confirm the fact stated earlier by Engels and Vogt,that the transverse two-plane correlation function of the O(4)model for lattice sizes about L=120 and small external fields h is very well described by a Gaussian approximation.However,we show that fits of not lower quality are provided by certain non-Gaussian approximation.We have also tested larger lattice sizes,up to L=512.The Fourier-transformed transverse and longitudinal two-point correlation functions have Goldstone mode singularities in the thermodynamic limit at k→0 and h=+0,i.e.,G_(⊥)(k)≈ak−λ_(⊥)and G_(||)(k)≈bk−λk,respectively.Here a and b are the amplitudes,k=|k|is the magnitude of the wave vector k.The exponentsλ_(⊥),λk and the ratio bM^(2)/a^(2),where M is the spontaneous magnetization,are universal according to the GFD(grouping of Feynman diagrams)approach.Here we find that the universality follows also from the standard(Gaussian)theory,yielding bM^(2)/a^(2)=(n−1)/16.Our MC estimates of this ratio are 0.06±0.01 for n=2,0.17±0.01 for n=4 and 0.498±0.010 for n=10.According to these and our earlier MC results,the asymptotic behavior and Goldstone mode singularities are not exactly described by the standard theory.This is expected from the GFD theory.We have found appropriate analytic approximations for G_(⊥)(k)and G_(||)(k),well fitting the simulation data for small k.We have used them to test the Patashinski-Pokrovski relation and have found that it holds approximately。

Spatial Correlation Function in Modular Networks

Due to the complexity of the interactions among the nodes of the complex networks,the properties of the networkmodules,to a large extent,remain unknown or unexplored.In this paper,we introduce the spatial correlation function Grs to describe the correlations among the modules of the weighted networks.In order to test the proposedmethod,we use ourmethod to analyze and discuss themodular structures of the ER random networks,scale-free networks and the Chinese railway network.Rigorous analysis of the existing data shows that the spatial correlation function Grs is suitable for describing the correlations among different networkmodules.Remarkably,we find that different networks display different correlations,especially,the correlation function Grs with different networks meets different degree distribution,such as the linear and exponential distributions.

Correlation of cognitive function with acetylcholinesterase activity and P300 event-related potential of patients with type 2 diabetes mellitus

BACKGROUND： At present, central cholinergic neuron system is regarded the most major structural basis of cognitive function. Changes in structure of cholinergic neuron system of brain and receptor expression after brain injury can cause cognitive impairment. OBJECTIVE＂ To comparatively observe the intelligence quotient （IQ）, latent period and wave amplitude of P300 event-related potential and the difference of activity of acetylcholinesterase （ACHE） in blood and cerebrospinal fluid between patients with type 2 diabetes mellitus and with non-diabetes mellitus, and analyze the correlation of IQ of cognitive impairment patients with diabetes mellitus with AChE activity, latent period and wave amplitude of P300 event-related potential in cerebrospinal fluid. DESIGN： Correlation analysis of contrast observation SETTING： Department of Endocrinology, Affiliated Hospital of Binzhou Medical College PARTICIPANTS： Totally 32 patients with type 2 diabetes mellitus who received the treatment in the Department of Endocrinology, Affiliated Hospital of Binzhou Medical College between April 2004 and April 2005 were recruited, serving as diabetes mellitus group. They, including 19 male and 13 female, aged 49 to 73 years, with disease course of 4 to 11 years, all met the diagnostic criteria of diabetes mellitus revised by World Health Organization in 1999. Another 30 patients with non-diabetes mellitus who homeochronously underwent lumbar anesthesia in the Department of Surgery and Department of Gynecology were recruited, serving as non-diabetes mellitus group. The 30 patients included 18 male and 12 female, and their age ranged from 46 to 71 years. Informed consents of detected items were obtained from the involved patients. METHODS： ① Evaluation,on IQ： The IQ of involved subjects was evaluated with Chinese Version of the Wechsler Adult Intelligence Scale revised by Gong Yao-xian （WAIS-RC）. WAIS-RC included 6 verbal subscales and 5 performance subscales. The test scores of the 11 subscales integrated into the scores of the whole scale, and the scores on the WAIS-RC included verbal IQ （VlQ）, performance IQ （PIQ） and full scale IQ （FIQ）. FIQ ≤79 scores indicated low IQ and FIQ≤69 indicated intelligence impairment. ② Detection of P300 wave： P300 wave was detected with evoked potential instrument （MYTOPRO, Italian）, and data of latent period and amplitude of P300 event-related potential were automatically shown by computer. ③ Detection of AChE activity in blood and cerebrospinal fluid： Activity of AChE of blood and cerebrospinal fluid was measured with biochemical methods by using CORNING-560 autoanalyzer.④Correlation analysis： Correlation of FIQ with AChE of cerebrospinal fluid and P300 wave of patients with type 2 diabetes mellitus was analyzed, t test was used in intergroup comparison and linear correlation analysis for relevant treatment. MAIN OUTCOME MEASURES： ① Comparison of IQ, latent period and wave amplitude of P300 wave as well as the activity of AChE between two groups. ② Analysis on the correlation of FIQ of patients with type 2 diabetes mellitus with AChE of cerebrospinal fluid and P300 wave. RESULTS： Thirty-two patients with diabetes mellitus and 30 non-diabetes mellitus participated in the result analysis. ①Comparison of IQ, latent period and wave amplitude of P300 wave as well as the activity of AChE between two groups： The scores of VIP, PIQ and FIQ of patients with type 2 diabetes mellitus were （97.4±10.4）. （92.6±8.4） and （95.2±9.7） scores, respectively; and those of patients with non-diabetes mellitus were （104.7±9.6）, （102.5±8.5）and（102.7±8.9） scores, respectively, and P 〈 0.05-0.01 was set in intergroup comparison. The latent period of P300 wave at points Fz , Cz and Pz of patients with type 2 diabetes mellitus was （370.8±41.8）.（371.5±39.1）and （375.1±43.1） ms, respectively, and that of patients with non-diabetes mellitus was （ 332.1 ±28.3 ）, （335.7 ±29.4）and （339.7 ±27.3） ms, respectively, and P 〈 0.01 was set in intergroup comparison; Wave amplitude of P300 of patients with type 2 diabetes mellitus was （8.6±4.1）,（8.6±4.0） and （7.7±4.0） μV, respectively and that of patients with non-diabetes mellitus was （11.9±4.1）,（11.5±4.4） and （10.9±5.0） μV, respectively , and P 〈 0.05-0.01 was set in intergroup comparison; The level of AChE in blood and cerebrospinal fluid of patients with type 2 diabetes mellitus was （235.61 ±50.34）and （17.89±4.46） μkat/L, respectively, which was significantly higher than that of patients with non-diabetes mellitus [（205.03±44.15）and （14.63±0.48） μkat /L, respectively], and P 〈 0.05-0.01 was set in the intergroup comparison. ② Correlation of FIQ value of patients with type 2 diabetes mellitus with AChE of cerebrospinal fluid and P300 wave： The value of FIQ was significantly negatively correlated with the AChE activity of cerebrospinal fluid （r=-0.588 1, P 〈 0.01 ）, significantly negatively correlated with the latent period at points Fz. C and Pz of P300 wave （r= -0.700 5, -0.689 4, -0.688 5, P 〈 0.01 ）, and significantly positively correlated with the amplitude at points Fz . Cz and Pz of P300 wave（r= 0.607 4,0.616 1,0.592 0,P 〈 0.01 ）. CONCLUSION： ① Cognitive impairment of patients with type 2 diabetes mellitus might be related to the increase of activity of AChE in cerebrospinal fluid. ②Combined application of examination of P300 wave and evaluation of IQ is more useful in deciding the state of cognitive function of patients with type 2 diabetes mellitus.

CSHINE for studies of HBT correlation in heavy ion reactions

The compact spectrometer for heavy ion experiment(CSHINE)is under construction for the study of isospin chronology via the Hanbury Brown–Twiss(HBT)particle correlation function and the nuclear equation of state of asymmetrical nuclear matter.The CSHINE consists of silicon strip detector(SSD)telescopes and large-area parallel-plate avalanche counters,which measure the light charged particles and fission fragments,respectively.In phase I,two SSD telescopes were used to observe 30 MeV/u 40Ar?197Au reactions.The results presented here demonstrate that hydrogen and helium were observed with high isotopic resolution,and the HBT correlation functions of light charged particles could be constructed from the obtained data.