Multi-Source Underwater DOA Estimation Using PSO-BP Neural Network Based on High-Order Cumulant Optimization

Due to the complex and changeable environment under water,the performance of traditional DOA estimation algorithms based on mathematical model,such as MUSIC,ESPRIT,etc.,degrades greatly or even some mistakes can be made because of the mismatch between algorithm model and actual environment model.In addition,the neural network has the ability of generalization and mapping,it can consider the noise,transmission channel inconsistency and other factors of the objective environment.Therefore,this paper utilizes Back Propagation(BP)neural network as the basic framework of underwater DOA estimation.Furthermore,in order to improve the performance of DOA estimation of BP neural network,the following three improvements are proposed.(1)Aiming at the problem that the weight and threshold of traditional BP neural network converge slowly and easily fall into the local optimal value in the iterative process,PSO-BP-NN based on optimized particle swarm optimization(PSO)algorithm is proposed.(2)The Higher-order cumulant of the received signal is utilized to establish the training model.(3)A BP neural network training method for arbitrary number of sources is proposed.Finally,the effectiveness of the proposed algorithm is proved by comparing with the state-of-the-art algorithms and MUSIC algorithm.

Existence and Uniqueness Results for a Fully Third-Order Boundary Value Problem

The boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have studied the boundary value problems of the complete third-order differential equations u′′′(t) = f (t,u(t),u′(t),u′′(t)). In this paper, we discuss the existence and uniqueness of solutions and positive solutions of the fully third-order ordinary differential equation on [0,1] with the boundary condition u(0) = u′(1) = u′′(1) = 0. Under some inequality conditions on nonlinearity f some new existence and uniqueness results of solutions and positive solutions are obtained.

Cumulative effects of excess high-normal alanine aminotransferase levels in relation to new-onset metabolic dysfunction-associated fatty liver disease in China

BACKGROUND Within the normal range,elevated alanine aminotransferase(ALT)levels are associated with an increased risk of metabolic dysfunction-associated fatty liver disease(MAFLD).AIM To investigate the associations between repeated high-normal ALT measurements and the risk of new-onset MAFLD prospectively.METHODS A cohort of 3553 participants followed for four consecutive health examinations over 4 years was selected.The incidence rate,cumulative times,and equally and unequally weighted cumulative effects of excess high-normal ALT levels(ehALT)were measured.Cox proportional hazards regression was used to analyse the association between the cumulative effects of ehALT and the risk of new-onset MAFLD.RESULTS A total of 83.13%of participants with MAFLD had normal ALT levels.The incidence rate of MAFLD showed a linear increasing trend in the cumulative ehALT group.Compared with those in the low-normal ALT group,the multivariate adjusted hazard ratios of the equally and unequally weighted cumulative effects of ehALT were 1.651[95%confidence interval(CI):1.199-2.273]and 1.535(95%CI:1.119-2.106)in the third quartile and 1.616(95%CI:1.162-2.246)and 1.580(95%CI:1.155-2.162)in the fourth quartile,respectively.CONCLUSION Most participants with MAFLD had normal ALT levels.Long-term high-normal ALT levels were associated with a cumulative increased risk of new-onset MAFLD.

基于RARE-Cumulant的互耦校正和DOA估计

基于四阶累计量及RARE(RAnk reducee quation)变换,结合均匀线阵互耦矩阵的特殊性,提出了一种新的互耦校正及波达方向估计算法。虽然四阶累计量比传统的二阶方法算法复杂,却扩展了阵列孔径,提高了在色噪声背景下DOA估计精度,而互耦系数并未因增加了虚拟阵元而增多。RARE变换将互耦系数与波达方向参量分离,有效地实现了多维参数估计的降维处理,减小了多维参量估计的计算量。仿真实验表明,在高斯色噪声背景下,本文方法计算量小,而且估计能力明显优于二阶去耦算法和传统的四阶方法。

CONVERGENCE PROPERTIES OF HIGHER-ORDER MOMENT AND CUMULANT ESTIMATES

The sample estimates of higher-order statistics are studied. Under certain conditions, the almost sure convergence of the third- and fourth-order moment and cumulant estimates of stationary processes is established. The rate of almost sure convergence is obtained for the sample estimates of third- and fourth-order moment and cumulant. Additionally, it is shown that the third- and fourth-order moment and cumulant estimates are asymptotic normal.

Oscillation Criteria for Third-order NonlinearNeutral Dynamic Equations on Time Scales

Many practical problems, such as those from electronic engineering, mechanicalengineering, ecological engineering, aerospace engineering and so on, need to bedescribed by dynamic equations on time scales, so it is important in theory andpractical significance to study these equations. In this paper, the oscillation andasymptotic behavior of third-order nonlinear neutral delay dynamic equations ontime scales are studied by using generalized Riccati transformation technique, integralaveraging methods and comparison theorems. The main purpose of this paperis to establish some new oscillation criteria for such dynamic equations. The newKamenev criteria and Philos criteria are given, and an example is considered toillustrate our main results.

Astronomical Cycles of the Late Permian Lopingian in South China and Their Implications for Third-Order Sea-Level Change

The late Permian(Lopingian)was a crucial climate transition period from the late Paleozoic Ice Age to the early Triassic of exceptionally high temperatures.However,the origins of the third-order sea-level changes during the Lopingian Epoch remain unclear.Here,we presented astronomically calibrated gamma-ray(GR)log and non-U GR(computed gamma ray or CGR)curves from the clastic and carbonate successions of well GFD-1 in the Pingle Depression of South China for studying the sea-level oscillations during the Lopingian.Spectral analyses of the 405 kyr-calibrated GR and CGR time data revealed periodicities close to about 405,about 100,about 44.2,about 35.1,about 21,and about 17.5 kyr,supporting the existence of Milankovitch forcing in the sedimentary records.A high-resolution astronomical time scale and high-resolution sedimentation rate curve of the Lopingian from well GFD-1 were constructed by cyclostratigraphic analysis.The eccentricity and obliquity amplitude modulation cycles suggested long periodicities of about 2.4 and about 1.2 myr,respectively.In the Wuchiapingian greenhouse of the Lopingian,the about 2.4 myr eccentricity oscillation controlled‘weak’glacio-eustasy and/or aquifer eustatic changes related to the global third-order sea-level changes and that a lowstand(W2)was initiated by an eccentricity oscillation minimum.In contrast,during the Changhsingian,which exhibited a cooling event,an about 1.2 myr obliquity cycle was probably strong,with the sea-level records highlighting the link between the‘icehouse’sea-level lowering(C2 and C1)and the obliquity nodes.Moreover,dynamic sedimentary noise model as an indicator of sea-level showed local third-order sea-level variations,the coevolution trends in the orbital power,global and local sea-level changes,and sedimentation rate had significant implications for establishing the global nature and synchronicity of these million-year-scale eustatic records and reconstructing the temporal depositional history at a regional scale.In addition,the volcanism and tectonism that continued into the early-middle Wuchiapingian probably led to a series of climate changes that drove the hydrological cycles not paced by the Milankovitch cycles.

Application of Three Order Cumulants in Fault Diagnosis

The three-order cumulants’ complex forms of different definitions include different coupling information of signals, and the information can be used to diagnose fault. In the experiment of pressure reducing valve’s fault diagnosis, through these different coupling information, the features of fault signals and normal signals were extracted by wavelet in different directions, then these features were inputted to diagnose the fault. The experiment shows that this method can achieve a satisfactory result.

CLASSIFICATION OF MPSK SIGNALS USING CUMULANT INVARIANTS

A new feature based on higher order statistics is proposed for classification of MPSKsignals, which is invariant with respect to translation (shift), scale and rotation transforms of MPSK signal constellations, and can suppress additive color or white Gaussian noise. Application of the new feature to classification of MPSK signals, at medium signal-to-noise ratio with specified sample size, results in high probability of correct identification. Finally, computer simulations and comparisons with existing algorithms are given.

Recognition Analysis and Simulation Implementation Based on High-Order Cumulants of Wireless Digital Modulation Mode

This paper mainly studies the data characteristics of high order cumulants using digitally modulated signals, and constructs the identification feature parameters that can distinguish the signal modulation type by the high-order cumulants data of the digital modulation signal. Set the identification signal modulation type determination threshold based on the value of the identification feature parameter. The identification feature parameter value of the signal modulation type is compared with the set determination threshold, to realize the recognition of digital modulation signal. This identification method is implemented based on MATLAB design, with a 2ASK (2-ary Amplitude Shift Keying) signal, 4ASK (4-ary Amplitude Shift Keying) signal, 2PSK (2-ary Phase Shift Keying) signal, 4PSK (4-ary Phase Shift Keying) signal, 2FSK (2-ary Frequency Shift Keying) signal, 4FSK (4-ary Frequency Shift Keying) signal. The second, fourth and sixth order cumulants of the six signals were analyzed. Calculate the selected identification feature parameter value and the determination threshold to identify the six signals. The six signals have made MATLAB identification simulation. Simulation results show that this method is feasible and has high recognition rate. Simulation results verify that such recognition methods maintain a high recognition rate under conditions with low signal-to-noise ratio. This identification method can be extended to more MASK (M-ary Amplitude Shift Keying), MPSK (M-ary Phase Shift Keying), MFSK (M-ary Frequency Shift Keying), MQAM (M-ary Quadrature Amplitude Modulation) signal identification.

Giant and light modifiable third-order optical nonlinearity in a free-standing h-BN film

Recently,hexagonal boron nitride(h-BN)has become a promising nanophotonic platform for on-chip information devices due to the practicability in generating optically stable,ultra-bright quantum emitters.For an integrated information-processing chip,high optical nonlinearity is indispensable for various fundamental functionalities,such as all-optical modulation,high order harmonic generation,optical switching and so on.Here we study the third-order optical nonlinearity of free-standing h-BN thin films,which is an ideal platform for on-chip integration and device formation without the need of transfer.The films were synthesized by a solution-based method with abundant functional groups enabling high third-order optical nonlinearity.Unlike the highly inert pristine h-BN films synthesized by conventional methods,the free-standing h-BN films could be locally oxidized upon tailored femtosecond laser irradiation,which further enhances the third-order nonlinearity,especially the nonlinear refraction index,by more than 20 times.The combination of the free-standing h-BN films with laser activation and patterning capability establishes a new promising platform for high performance on-chip photonic devices with modifiable optical performance.

Existence of Multiple Positive Solutions for Third-Order Three-Point Boundary Value Problem

In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boundary value problem has at least three positive solutions are obtained. An example illustrating our main result is given. Moreover, some previous results will be improved significantly in our paper.

Ecological risk assessment and early warning of heavy metal cumulation in the soils near the Luanchuan molybdenum polymetallic mine concentration area,Henan Province,central China

The Luanchuan molybdenum polymetallic mine concentration area is rich in mineral resources and has a long history of mining.The environmental impact of long-term mining activities cannot be ignored.It is of great significance to study the ecological risk and the accumulation trends of heavy metals in the soil of mining areas for scientific prevention and control of heavy metal pollution.Taking the Taowanbeigou River Basin in the mine concentration area as the research object,the ecological pollution risk and cumulative effect of heavy metals in the soil of the basin were studied by using the comprehensive pollution index method,potential ecological risk assessment method and geoaccumulation index method.On this basis,the cumulative exceeding years of specific heavy metals were predicted by using the early warning model.The comprehensive potential ecological risk of heavy metals in the soil near the Luanchuan mine concentration area is moderate,and the single element Cd is the main ecological risk factor,with a contribution rate of 53.6%.The overall cumulative degrees of Cu and Pb in the soil are“none-moderate”,Zn and Cd are moderate,Mo has reached an extremely strong cumulative level,Hg,As and Cr risks are not obvious,and the overall cumulative risks order is Mo>Cd>Zn>Cu>Pb>Hg.According to the current accumulation rate and taking the risk screening values for soil contamination of agricultural land as the reference standard,the locations over standard rates of Cu,Zn and Cd will exceed 78%in 90years,and the over standard rate of Pb will reach approximately 57%in 200 years.The cumulative exceeding standard periods of As,Cr and Hg are generally long,which basically indicates that these elements do not pose a significant potential threat to the ecological environment.Mining activities will accelerate the accumulation of heavy metals in soil.With the continuous development of mining activities,the potential pollution risk of heavy metals in the soil of mining areas will also increase.

A Highly Compact Third-Order Silicon Elliptical Micro-Ring Add-Drop Filter with a Large Free Spectral Range

We demonstrate a highly compact third-order elliptical micro-ring add-drop filter based on a silicon-on-insulator wafer.The elliptical micro-ring resonator has a major radius of 6μm(minor radius of 4.112 μm)and a large free spectral range of 18 nm.Experimental results show a box-like channel dropping response,which has a 3 dB bandwidth of ~2.7 nm,high out-of-band signal rejection of around 40 dB and a very low drop loss(<0.5 dB).Simulation agrees well with the experiments.The footprint of the whole chip is only 0.0003 mm^2.

Functional Integrals and Variational-Cumulant Expansion in sine-Gordon-Thirring Model

The free energy in 1D sine-Gordon-Thirring model with impurity coupling is studied by means of functionalintegrals and variational-cumulant expansion methods.Two variational parameters are introduced to evaluate free energyand statistical averages.It is shown that the non-perturbation method of functional integrals can be applied to strong-coupling range of fermion systems.

A Cumulant-Based Beamforming Algorithm for CDMA Frequency-nonselective Fading Channel

A cumulant\|based beamforing technique for synchronous CDMA system with decorrelator is presented. With decorrelating detector the proposed algorithm has the advantages that the steering vector of desired user’s can be estimated independently by eliminating all the other resolved signal interferences. Furthermore employing cumulant\|based signal processing technique the steering vector of the decoupled signals can be estimated blindly. Simulation results show that the cumulant\|based beamformer demonstrates excellent performance.

Third-order elastic, piezoelectric, and dielectric constants

The definitions of the third-order elastic,piezoelectric,and dielectric constants and the properties of the associated tensors are discussed.Based on the energy conservation and coordinate transformation,the relations among the third-order constants are obtained.Furthermore,the relations among the third-order elastic,piezoelectric,and dielectric constants of the seven crystal systems and isotropic materials are listed in detail.These third-order constants relations play an important role in solving nonlinear problems of elastic and piezoelectric materials.It is further found that all third-order piezoelectric constants are 0 for 15 kinds of point groups,while all third-order dielectric constants are 0 for 16 kinds of point groups as well as isotropic material.The reason is that some of the point groups are centrally symmetric,and the other point groups are high symmetry.These results provide the foundation to measure these constants,to choose material,and to research nonlinear problems.Moreover,these results are helpful not only for the study of nonlinear elastic and piezoelectric problems,but also for the research on flexoelectric effects and size effects.

ANALYSIS OF A CUMULANT-BASED 2D-RAKE RECEIVER FOR CDMA SYSTEM OVER FREQUENCY-SELECTIVE FADING CHANNELS

The conventional 2D Rake receivers for code division multiple access (CDMA) system over frequency selective fading channels are generally based on the second order statistics while assuming perfect array conditions. However, the sensor response, location uncertainty, and the use of sample statistics can severely degrade the performance of second order statistics processing. And in practical application, it is impossible to calibrate the array frequently. In this paper a cumulant based 2D Rake receiver for synchronous CDMA system with decorrelator is presented. Decorrelating is a multi user detection approach that not only provides a fundamental solution to the mutual interference problem in CDMA communications but also makes it convenient for the decoupled signal to be processed spatially and temporally. High order signal processing has some inherent advantages over that of second order. Employing second order statistics it is impossible to estimate source steering vector blindly, while employing higher than second order cumulants, this purpose can be achieved. The performance analysis shows that employing cumulant based signal processing technique the proposed 2D Rake receiver is blind and demonstrates excellent performance.

ADAPTIVE ALGORITHM FOR CONSISTENTMA PARAMETER ESTIMATION VIATHIRD ORDER CUMULANT

This paper addresses the problem of adaptive,consistent parameter estimation for a MA model from the 3rd order cumulant of the system output. The proposed adaptive algorithm is derived by using the new linear equation system (J. K. Tugnait, 1990), which is proved to have unique solution,and hence guarantees the consistence of the MA parameters. Simulation results are provided to show the performance of the new algorithm.

Joint estimation of DOA, frequency, and polarization based on cumulants and UCA

A joint estimation algorithm of direction of arrival (DOA), frequency, and polarization, based on fourth-order cumulants and uniform circular array (UCA) of trimmed vector sensors is presented for narrowband non-Gaussian signals. The proposed approach, which is suitable for applications in arbitrary Gaussian noise environments, gives a closed-form representation of the estimated parameters, without spectral peak searching. An efficient method is also provided for elimination of cyclic phase ambiguities. Simulations are presented to show the performance of the algorithm.