Stability and accuracy of central difference method for real-time dynamic substructure testing considering mass participation coefficient

For real-time dynamic substructure testing(RTDST),the influence of the inertia force of fluid specimens on the stability and accuracy of the integration algorithms has never been investigated.Therefore,this study proposes to investigate the stability and accuracy of the central difference method(CDM)for RTDST considering the specimen mass participation coefficient.First,the theory of the CDM for RTDST is presented.Next,the stability and accuracy of the CDM for RTDST considering the specimen mass participation coefficient are investigated.Finally,numerical simulations and experimental tests are conducted for verifying the effectiveness of the method.The study indicates that the stability of the algorithm is affected by the mass participation coefficient of the specimen,and the stability limit first increases and then decreases as the mass participation coefficient increases.In most cases,the mass participation coefficient will increase the stability limit of the algorithm,but in specific circumstances,the algorithm may lose its stability.The stability and accuracy of the CDM considering the mass participation coefficient are verified by numerical simulations and experimental tests on a three-story frame structure with a tuned liquid damper.

The difference analysis of physical-mechanical properties of sediments in the central South Yellow Sea and Zhe-Min coastal area in China

The difference analysis of physical-mechanical properties of muddy sediments is made in the central South Yellow Sea and the Zhe-Min（Zhejiang Province to Fujian Province of China） coastal area. The results show that sediments in the two regions are both dominated by mud. There are perfect negative power function correlations between the water content and the density, the compression coefficient and the compression modulus; a good positive power function correlation between the liquid limit and the plastic limit, a perfect positive linear correlation between the water content and the void ratio, and a perfect polynomial function correlation between the miniature vane shear strength and the pocket penetration resistance. In general, compared with sediments in the Zhe-Min coastal area, sediments in the central South Yellow Sea possess high water content, high void ratio,low density, high plasticity, high compressibility, low shear strength. The causes of the differences between physical-mechanical properties of sediments are analyzed from the topographic features, material sources,hydrodynamic conditions, deposition rate, and material composition. Compared with the Zhe-Min coastal area,the central South Yellow Sea is far from the Mainland and low-lying; has poor hydrodynamic condition; the materials diffused to the area are less and dominated by fine clay, have the high content of smectite and organic matters. These factors lead to sediments of the central South Yellow Sea has the higher water content, the higher plasticity, the lower density, and the lower strength than sediments in the Zhe-Min coastal area.

Combined Estimation of Vehicle Dynamic State and Inertial Parameter for Electric Vehicles Based on Dual Central Difference Kalman Filter Method

Distributed drive electric vehicles(DDEVs)possess great advantages in the viewpoint of fuel consumption,environment protection and traffic mobility.Whereas the effects of inertial parameter variation in DDEV control system become much more pronounced due to the drastic reduction of vehicle weights and body size,and inertial parameter has seldom been tackled and systematically estimated.This paper presents a dual central difference Kalman filter(DCDKF)where two Kalman filters run in parallel to simultaneously estimate vehicle different dynamic states and inertial parameters,such as vehicle sideslip angle,vehicle mass,vehicle yaw moment of inertia,the distance from the front axle to centre of gravity.The proposed estimation method only integrates and utilizes real-time measurements of hub torque information and other in-vehicle sensors from standard DDEVs.The four-wheel nonlinear vehicle dynamics estimation model considering payload variations,Pacejka tire model,wheel and motor dynamics model is developed,the observability of the DCDKF observer is analysed and derived via Lie derivative and differential geometry theory.To address system nonlinearities in vehicle dynamics estimation,the DCDKF and dual extended Kalman filter(DEKF)are also investigated and compared.Simulation with various maneuvers are carried out to verify the effectiveness of the proposed method using Matlab/Simulink-CarsimR.The results show that the proposed DCDKF method can effectively estimate vehicle dynamic states and inertial parameters despite the existence of payload variations and variable driving conditions.This research provides a boot-strapping procedure which can performs optimal estimation to estimate simultaneously vehicle system state and inertial parameter with high accuracy and real-time ability.

High-resolution central difference scheme for the shallow water equations

A two-dimensional nonoscillatory central difference scheme was extended to the shallow water equations. A high-resolution numerical method for solving the shallow water equations was presented. In order to prevent oscillation, the nonlinear limiter is employed to approximate the discrete slopes. The main advantage of the presented method is simplicity comparable with the upwind schemes. This method does not require Riemann solvers or some form of flux difference splitting methods. Furthermore, the discrete derivatives of flux can be approximated by the component-wise approach and thus the computation of Jacobian can be avoided. The method retains high resolution and high accuracy similar to the upwind results. It is applied to simulating several tests, including circular dam-break problem, shock focusing problem and partial dam-break problem. The results are in good agreement with the numerical results obtained by other methods. The simulated results also demonstrate that the presented method is stable and efficient.

ADHESIVE CONTACT PROBLEM OF AXISYMMETRIC MINIATURE CIRCULAR PLATES WITH CENTRAL RIGID BUMP

Considering the adhesive effect and geometric nonlinearity, the adhesive contact between an elastic substrate and a clamped miniature circular plate with two different central rigid bumps under the action of uniform transverse pressure and in-plane tensile force in the radial direction was analyzed. And an analytical solution is presented by using the perturbation method. The relation of surface adhesive energies with critical load to detach the contacted surfaces is obtained. In the numerical results, the effects of adhesive energy, in-plane tensile force, rigid bump size and contact radius on the critical load are discussed, and the relation of critical contact radius with the gap between the central rigid bump and the substrate for different adhesive energies is investigated.

Effect of intervention treatment from different stages on prognosis in children with central coordination disturbance

BACKGROUND： Central coordination disturbance is regarded as the early-stage symptom of brain injury-induced cerebral palsy. This disease manifests itself as motor disorder, abnormal attitudinal reflex and muscular tension. Early intervention may improve its prognosis. OBJECTIVE： To observe the effects of intervention treatment from different stages on the prognosis of central coordination disturbance following brain injury in children patients. DESIGN： A contrast observation experiment SETTING： Department of Neurology and Rehabilitation, Urumqi Children＇s Hospital PARTICIPANTS ： Totally 151 children who were diagnosed as central coordination disturbance from January 2002 to December 2003 in the Department of Neurology and Rehabilitation of Urumqi Children＇s Hospital were recruited. All the children patients, including 101 male and 50 female, aged from 3 months to 1 year old, met the diagnosis criteria of central coordination disturbance from Vojta. They were divided into slight, moderate and severe abnormity according to Vojta attitudinal reflex. All 151 patients were divided into 2 groups according to their age at diagnosis： 3-6 months old group （n=74）, 62 severe, 10 moderate and 2 slight; 7-12 months old group （n=77）, 66 severe, 7 moderate and 4 slight. All the relatives of children patients were informed of the experiment. METHODS： ① Both groups received physical training （PT） as the main treatment; Hand training was given if necessary. All of the patients received additional hyperbaric oxygen therapy, bioelectric therapy, scalp acupuncture, drug treatment and family training. The importance of integration of hospital and family based rehabilitation was stressed. Those who did not catch up with the normal development or had abnormal reflexes continued to receive treatment. ② Around the age of 2 years old, all children did a final evaluation using Bayley Scales of Infant Development （BSID）. Mental development index （MDI） and physical development index （PDI） were taken as evaluative criteria. Children with scores 80 and above on MDI and PDI were considered to have normal motor and mental development; 79 and below were considered delayers. The Diagnostic Criteria of Cerebral Palsy and Infantecondary School Social Adaptation Scale were used in the final evaluation[scores ≤5 was extremely severe （extremely severe cerebral palsy）, 6 was severe（severe cerebral palsy）, 7 was moderate（moderate cerebral palsy）, 8 was slight（slight cerebral palsy）, 9 was borderline（slight cerebral palsy）, 10 was normal, 11 was above average, 12 was excellent and ≥13 was extremely excellent]. ③ Final evaluative results of 2 groups were compared. And u test was used for the comparison of Bayley development index and Chi-square test for the comparison of normalization rate. MAIN OUTCOME MEASURES： BSID MDI and PDI as well as the normalization rate of motor function and mental behavior of children patients at 2 years old. RESULTS： Totally 151 children patients entered the stage of result analysis. ①Two groups of children patients were given integrated rehabilitation therapy , and evaluated at 2 years old . The 3-6 months old group had higher MDI and PDI than the 7-12 months old group （91.81＋19.99 vs 71.93＋18.98;91.55＋23.61 vs 68.95＋23.51, u=6.265,5.894,P 〈 0.01 ）.②After being given integrated rehabilitation therapy, children patients of 3-6 months old group had significantly higher normalization rate of motor function and mental behavior than 7-12 months old group （73% ,27%,X2=29.723 9,P 〈 0.01 ）. ③Six slight and 17 moderate central coordination disturbance children of 2 groups all completely recovered; After intervention treatment, among 128 severe central coordination disturbance children, 52 recovered and 76 were still abnormal, in which, 43 slight cerebral palsy, 18 moderate cerebral palsy, 5 severe cerebral palsy and 10 extremely severe cerebral palsy. CONCLUSION： To perform integrated intervention treatment before 6 months old can better improve and promote mental and physical development levels of children patients with central coordination disturbance after brain injury than 6 months later.

Numerical Solution of Parabolic in Partial Differential Equations (PDEs) in One and Two Space Variable

In this paper, we shall be concerned with the numerical solution of parabolic equations in one space variable and the time variable t. We expand Taylor series to derive a higher-order approximation for Ut. We begin with the simplest model problem, for heat conduction in a uniform medium. For this model problem, an explicit difference method is very straightforward in use, and the analysis of its error is easily accomplished by the use of a maximum principle. As we shall show, however, the numerical solution becomes unstable unless the time step is severely restricted, so we shall go on to consider other, more elaborate, numerical methods which can avoid such a restriction. The additional complication in the numerical calculation is more than offset by the smaller number of time steps needed. We then extend the methods to problems with more general boundary conditions, then to more general linear parabolic equations. Finally, we shall discuss the more difficult problem of the solution of nonlinear equations.

A quadratic linear-parabolic model-based EEG classification to detect epileptic seizures

The two-point central difference is a common algorithm in biological signal processing and is particularly useful in analyzing physiological signals.In this paper,we develop a model-based classification method to detect epileptic seizures that relies on this algorithm to filter electroencephalogram(EEG) signals.The underlying idea was to design an EEG filter that enhances the waveform of epileptic signals.The filtered signal was fitted to a quadratic linear-parabolic model using the curve fitting technique.The model fitting was assessed using four statistical parameters,which were used as classification features with a random forest algorithm to discriminate seizure and non-seizure events.The proposed method was applied to 66 epochs from the Children Hospital Boston database.Results showed that the method achieved fast and accurate detection of epileptic seizures,with a92% sensitivity,96% specificity,and 94.1% accuracy.

UNSTEADY/STEADY NUMERICAL SIMULATION OF THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON ARTIFICIAL COMPRESSIBILITY

A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The numerical flux of semi-discrete equations is computed by using the Roe approximation. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The algebraic turbulence model of Baldwin-Lomax is ulsed in this work. As examples, the solutions of flow through two dimensional flat, airfoil, prolate spheroid and cerebral aneurysm are computed and the results are compared with experimental data. The results show that the coefficient of pressure and skin friction are agreement with experimental data, the largest discrepancy occur in the separation region where the lagebraic turbulence model of Baldwin-Lomax could not exactly predict the flow.

A new optimal approach to segmentation of 2D range scans to line sections

In order to obtain a compact and exact representation of 2D range scans,UKF(unscented Kalman filter) and CDKF(central difference Kalman filter) were proposed for extracting the breakpoint of the laser data. Line extraction was performed in every continuous breakpoint region by detecting the optimal angle and the optimal distance in polar coordinates,and every breakpoint area was constructed with two points. As a proof to the method,an experiment was performed by a mobile robot equipped with one SICK laser rangefinder,and the results of UKF/CDKF in breakpoint detection and line extraction were compared with those of the EKF(extended Kalman filter) . The results show that the exact geometry of the raw laser data of the environments can be obtained by segmented raw measurements(combining the proposed breakpoint detection approach with the line extraction method) ,and method UKF is the best one compared with CDKF and EKF.

Maneuvering target tracking algorithm based on CDKF in observation bootstrapping strategy

The selection and optimization of model filters affect the precision of motion pattern identification and state estimation in maneuvering target tracking directly.Aiming at improving performance of model filters,a novel maneuvering target tracking algorithm based on central difference Kalman filter in observation bootstrapping strategy is proposed.The framework of interactive multiple model(IMM) is used to realize identification of motion pattern,and a central difference Kalman filter(CDKF) is selected as the model filter of IMM.Considering the advantage of multi-sensor fusion method in improving the stability and reliability of observation information,the hardware cost of the observation system for multiple sensors is adopted,meanwhile,according to the data assimilation technique in Ensemble Kalman filter(En KF),a bootstrapping observation set is constructed by integrating the latest observation and the prior information of observation noise.On that basis,these bootstrapping observations are reasonably used to optimize the filtering performance of CDKF by means of weight fusion way.The object of new algorithm is to improve the tracking precision of observed target by the multi-sensor fusion method without increasing the number of physical sensors.The theoretical analysis and experimental results show the feasibility and efficiency of the proposed algorithm.

Simulation on venting process and valve opening control method for gas trunk pipelines

Determining the venting time of a gas trunk pipeline segment provides an important basis for formulating an emergency plan in the advent of unexpected accidents.As the natural gas venting process corresponds to the transient flow,it is necessary to establish a transient hydraulic-thermal simulation model in order to determine the venting time.In this paper,based on two kinds of venting scenarios in which there is only one venting point in the venting system of a gas trunk pipeline segment—namely,where the venting point is either at one of the two ends or at the junction of two gas trunk pipeline segments—transient hydraulic-thermal simulation models are established.The models consist of gas flow governing equations,the gas state equation,gas physical property equations,initial conditions,and appropriate boundary conditions.The implicit central difference method is used to discretize the gas flow partial differential equations,and the trust-region-dogleg algorithm is used to solve the equations corresponding to each time step,in order to dynamically simulate the whole venting process.The judgment condition for the end of the venting process is that the average pressure of gas trunk pipeline segment is less than 0.11 MPa(actual pressure).Comparing the simulation results of the proposed model with those of the OLGA software and real operational data,we find that the venting time error is less than 10%.On this basis,a venting valve opening control principle is proposed,which prevents the venting noise from exceeded the specified noise value(85 d B)in the venting design of domestic gas pipeline projects.The established calculation model for venting time(dynamic simulation model)for a gas trunk pipeline segment and the proposed opening control principle of venting valve provide reference for the optimal operation of gas pipeline venting systems.

Comments on Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD

The explicit compact difference scheme, proposed in Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD by Lin et al., published in Applied Mathematics and Mechanics （English Edition）, 2007, 28（7）, 943-953, has the same performance as the conventional finite difference schemes. It is just another expression of the conventional finite difference schemes. The proposed expression does not have the advantages of a compact difference scheme. Nonetheless, we can more easily obtain and implement compared with the conventional expression in which the coefficients can only be obtained by solving equations, especially for higher accurate schemes.

Finite Di erence Method for Riesz Space Fractional Advection-dispersion Equation with Fractional Robin Boundary Condition

In this paper,a Riesz space fractional advection-dispersion equation with fractional Robin boundary condition is considered.By applying the fractional central di erence formula and the weighted and shifted Grunwald-Letnikov formula,we derive a weighted implicit nite difference scheme with accuracy O(△t^2+h^2).The solvability,stability,and convergence of the proposed numerical scheme are proved.A numerical example is presented to confirm the accuracy and efficiency of the scheme.

A Numerical Algorithm for the Caputo Tempered Fractional Advection-Diffusion Equation

By transforming the Caputo tempered fractional advection-diffusion equation into the Riemann–Liouville tempered fractional advection-diffusion equation,and then using the fractional-compact Grünwald–Letnikov tempered difference operator to approximate the Riemann–Liouville tempered fractional partial derivative,the fractional central difference operator to discritize the space Riesz fractional partial derivative,and the classical central difference formula to discretize the advection term,a numerical algorithm is constructed for solving the Caputo tempered fractional advection-diffusion equation.The stability and the convergence analysis of the numerical method are given.Numerical experiments show that the numerical method is effective.

A numerical study of 1-D nonlinear P-wave propagation in solid

Two central schemes of finite difference (FD) up to different accuracy orders of space sampling step Dx (Fourth order and Sixth order respectively) were used to study the 1-D nonlinear P-wave propagation in the nonlinear solid media by the numerical method. Distinctly different from the case of numerical modeling of linear elastic wave, there may be several difficulties in the numerical treatment to the nonlinear partial differential equation, such as the steep gradients, shocks and unphysical oscillations. All of them are the great obstacles to the stability and conver-gence of numerical calculation. Fortunately, the comparative study on the modeling of nonlinear wave by the two FD schemes presented in the paper can provide us with an easy method to keep the stability and convergence in the calculation field when the product of the absolute value of nonlinear coefficient and the value of u/x are small enough, namely, the value of bu/x is much smaller than 1. Several results are founded in the numerical study of nonlinear P-wave propagation, such as the waveform aberration, the generation and growth of harmonic wave and the energy redistribution among different frequency components. All of them will be more violent when the initial amplitude A0 is larger or the nonlinearity of medium is stronger. Correspondingly, we have found that the nonlinear P-wave propagation velocity will change with different initial frequency f of source wave or the wave velocity c (equal to the P-wave velocity in the same medium without considering nonlinearity).

A Spectral Method for Convection-Diffusion Equations

In the practical problems such as nuclear waste pollution and seawater intrusion etc., many problems are reduced to solving the convection-diffusion equation, so the research of convection-diffusion equation is of great value. In this work, a spectral method is presented for solving one and two dimensional convection-diffusion equation with source term. The finite difference method is also used to solve the convection diffusion equation. The numerical experiments show that the spectral method is more efficient than other methods for solving the convection-diffusion equation.

Multidomain Hybrid Direct DG and Central Difference Methods for Viscous Terms in Hyperbolic-Parabolic Equations

A class of multidomain hybrid methods of direct discontinuous Galerkin(DDG)methods and central difference(CD)schemes for the viscous terms is pro-posed in this paper.Both conservative and nonconservative coupling modes are dis-cussed.To treat the shock wave,the nonconservative coupling mode automatically switch to conservative coupling mode to preserve the conservative property when discontinuities pass through the artificial interface.To maintain the accuracy of the hybrid methods,the Lagrange interpolation polynomials and their derivatives are reconstructed to handle the coupling cells in the DDG subdomain,while the values of ghost points for the CD subdomain are calculated by the approximate polynomials from the DDG methods.The linear stabilities of these methods are demonstrated in detail through von-Neumann analysis.The multidomain hybrid DDG and CD meth-ods are then extended to one-and two-dimensional hyperbolic-parabolic equations.Numerical results validate that the multidomain hybrid methods are high-order ac-curate in the smooth regions,robust for viscous shock simulations and capable to save computational cost.

CAFUNeT:A small infrared target detection method in complex backgrounds

Small infrared target detection has widespread applications in various fields including military,aviation,and medicine.However,detecting small infrared targets in complex backgrounds remains challenging.To detect small infrared targets,we propose a variable-structure U-shaped network referred as CAFUNet.A central differential convolution-based encoder,ASPP,an Attention Fusion module,and a decoder module are the critical components of the CAFUNet.The encoder module based on central difference convolution effectively extracts shallow detail information from infrared images,complemented by rich contextual information obtained from the deep features in the decoder module.However,the direct fusion of the shallow detail features with semantic features may lead to feature mismatch.To address this,we incorporate an Attention Fusion(AF)module to enhance the network performance further.We performed ablation studies on each module to evaluate its effectiveness.The results show that our proposed algorithm outperforms the state-of-the-art methods on publicly available datasets.

ASSESSMENT OF A CENTRAL DIFFERENCE FINITE VOLUME SCHEME FOR MODELING OF CAVITATING FLOWS USING PRECONDITIONED MULTIPHASE EULER EQUATIONS

A numerical treatment for the prediction of cavitating flows is presented and assessed. The algorithm uses the preconditioned multiphase Euler equations with appropriate mass transfer terms. A central difference finite volume scheme with suitable dissipation terms to account for density jumps across the cavity interface is shown to yield an effective method for solving the multiphase Euler equations. The Euler equations are utilized herein for the cavitation modeling, because some certain characteristics of cavitating flows can be obtained using the solution of this system of equations with relative low computational effort. In addition, the Euler equations are appropriate for the assessment of the numerical method used, because of the sensitivity of the solution to the numerical instabilities. For this reason, a sensitivity study is conducted to evaluate the effects of various parameters, such as numerical dissipation coefficients and grid size, on the accuracy and performance of the solution. The computations are performed for steady cavitating flows around the NACA 0012 and NACA 66 （MOD） hydrofoils and also an axisymmetric hemispherical fore-body under different conditions and the results are compared with the available numerical and experimental data. The solution procedure presented is shown to be accurate and efficient for predicting steady sheet- and super-cavitation for 2D/axisymmetric geometries.