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.

Influence of Noise on Time Evolution of Intensity Correlation Function

Using the linear approximation method, we have studied how the correlation function C（t） of the laser intensity changes with time in the loss-noise model of the single-mode laser driven by the colored pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts. We have found that when the pump noise self-correlation time T changes, （i） in the case of r 〈〈 1, the C（t） vs. t curve experiences a changing process from the monotonous descending to monotonous rise, and finally to the appearance of a maximum; （ii） in the case of r 〉〉 1, the curve only exhibits periodically surging with descending envelope. When r 〈〈 i and T does not change, with the increase of the pump noise intensity P, the curve experiences a repeated changing process, that is, from the monotonous descending to the appearance of a maximum, then to monotonous rise, and finally to the appearance of a maximum again. With the increase of the quantum noise intensity O,, the curve experiences a changing process from the monotonous rise to the appearance of a maximum, and finally to the monotonous descending. The increase of the quantum noise with cross-correlation between the real and imaginary parts will lead to the fall of the whole curve, but not affect the form of the time evolution of C（t）.

Criterion for Blind Signals Separation Based on Correlation Function

Blind separation of source signals usually relies either on the condition of statistically independence or involving their higher-order cumulants. The model of two channels signal separation is considered. A criterion based on correlation functions is proposed. It is proved that the signals can be separated, using only the condition of noncorrelation. An algorithm is derived, which only involves the solution to quadric nonlinear equations.

Walsh Spectral Characteristics and the Auto-Correlation Function Characteristics of Forming Orthomorphic Permutations of Multi-Output Functions

Orthomorphic permutations have good characteristics in cryptosystems. In this paper, by using of knowledge about relation between orthomorphic permutations and multi-output functions, and conceptions of the generalized Walsh spectrum of multi-output functions and the auto-correlation function of multi-output functions to investigate the Walsh spectral characteristics and the auto-correlation function characteristics of orthormophic permutations, several results are obtained.

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.

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.

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.

Intensity Correlation Function of a Single-Mode Laser Driven by Colored Cross-Correlation Noises in Modulation of a Bias Signal

By using the linear approximation method, the intensity correlation function is calculated for a single-mode laser modulated by a bias signal and driven by colored pump and quantum noises with colored cross-correlation. We found that, when the correlation time between the two noises is very short, the behavior of the intensity correlation function versus the time, in addition to decreasing monotonously, also exhibits several cases, such as one maximum, one minimum, and two extrema. When the correlation time between the two noises is very long, the behavior of the intensity correlation function exhibits oscillation and the envelope is similar to the case of short cross-correlation time.

Boundary Correlation Functions of the gl(1|1) Supersymmetric Vertex Model

The gl（1/1） supersymmetric vertex model with domain wall boundary conditions （DWBC） on an N × N square lattice is considered. We derive the reduction formulae for the one-point boundary correlation functions of the model. The determinant representation for the boundary correlation functions is also obtained.

Double differential cross sections for ionization of H by 75 keV proton impact:Assessing the role of correlated wave functions

The effect of final-state dynamic correlation is investigated for ionization of atomic hydrogen by 75-keV proton impact by analyzing double differential cross sections.The final state is represented by a continuum correlated wave(CCW-PT)function which accounts for the interaction between the projectile and the target nucleus(PT interaction).The correlated final state is nonseparable solutions of the wave equation combining the dynamics of the electron motion relative to the target and projectile,satisfying the Redmond’s asymptotic conditions corresponding to long range interactions.The transition matrix is evaluated using the CCW-PT function and the undistorted initial state.Both the correlation effects and the PT interaction are analyzed by the present calculations.The convergence of the continuous correlated final state is examined carefully.Our results are compared with the absolute experimental data measured by Laforge et al.[Phys.Rev.Lett.103,053201(2009)]and Schulz et al.[Phys.Rev.A 81,052705(2010)],as well as other theoretical models(especially the results of the latest non perturbation theory).We have shown that the dynamic correlation plays an important role in the ionization of atomic hydrogen by proton impact.While overall agreement between theory and the experimental data is encouraging,detailed agreement is still lacking.However,such an analysis is meaningful because it provides valuable information about the dynamical correlation and PT interaction in the CCW-PT theoretical model.

The Influence of the Exchange-Correlation Functional on the Non-Interacting Kinetic Energy and Its Implications for Orbital-Free Density Functional Approximations

In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potential depends on the density only,the individual parts,the Pauli kinetic energy and the exchange-correlation energy,however,are orbital dependent and as such mutually influence each other.The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy.The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the orderof a few Hartrees.For chemical purposes,however,the energetic performance as a function of the nuclear coordinates is much more important than total energies.Therefore,the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide.The data reveals that,the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances.Therefore,the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.

Correlation Degree and Correlation Coefficient of Multi-Output Functions

We present definitions of the correlation degree and correlation coefficient of multi-output functions. Two relationships about the correlation degree of multi-output functions are proved. One is between the correlation degree and independency, the other is between the correlation degree and balance. Especially the paper discusses the correlation degree of affine multioutput functions. We demonstrate properties of the correlation coefficient of multi-output functions. One is the value range of the correlation coefficient, one is the relationship between the correlation coefficient and independency, and another is the sufficient and necessary condition that two multi-output functions are equivalent to each other.

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.

Chrestenson Spectrum and Auto-Correlation Function of Inverse Permutations of Quick Trickle Permutations

In this paper, a sufficient and necessary condition of quick trickle permutations is given from the point of inverse permutations. The bridge is built between quick trickle permutations and m-value logic functions. By the methods of the Chrestenson spectrum of m-value logic functions and the auto-correlation function of m-value logic functions to investigate the Chrestenson spectral characteristics and the auto-correlation function charac- teristics of inverse permutations of quick trickle permutations, a determinant arithmetic of quick trickle permutations is given. Using the results, it becomes easy to judge that a permutation is a quick trickle permutation or not by using computer. This gives a new pathway to study constructions and enumerations of quick trickle permutations.

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.

ENUMERATING CORRELATION-IMMUNE BOOLEAN FUNCTIONS OF ORDER ONE

A large class of linear structural functions(LSF) satisfying the condition of correlational immunity of order one are constructed by studying the linear structural Boolean functions. With these new founded functions, the known enumeration bounds of correlation-immune functions of order one are greatly improved. In fact, the best, up to now, lower bound is found.

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.