Research on Comparison and Evaluation Studies of Several Smoothing Denoising Method Based on γ-ray Spectrum Detector

The extraction of spectral parameters is very difficult because of the limited energy resolution for NaI （TI） gamma-ray detectors. For statistical fluctuation of radioactivity under complex environment, some smoothing filtering methods are proposed to solve the problem. These methods include adopting method of arithmetic moving average, center of gravity, least squares of polynomial, slide converter of discrete funcion convolution etc. The process of spectrum data is realized, and the results are assessed in H/FWHM（ Peak High/Full Width at Half Maximum） and peak area based on the Matlab programming. The results indicate that different methods smoothed spectrum have respective superiority in different ergoregion, but the Gaussian function theory in discrete function convolution slide method is used to filter the complex y-spectrum on Embedded system nlatform, and the statistical fluctuation of y-snectrum filtered wall.

A Smoothing Newton Method for the Box Constrained Variational Inequality Problems

The box constrained variational inequality problem can be reformulated as a nonsmooth equation by using median operator.In this paper,we present a smoothing Newton method for solving the box constrained variational inequality problem based on a new smoothing approximation function.The proposed algorithm is proved to be well defined and convergent globally under weaker conditions.

A Smoothing SAA Method for a Stochastic Linear Complementarity Problem

Utilizing the well-known aggregation technique, we propose a smoothing sample average approximation （SAA） method for a stochastic linear complementarity problem, where the underlying functions are represented by expectations of stochastic functions. The method is proved to be convergent and the preliminary numerical results are reported.

The use of the node-based smoothed finite element method to estimate static and seismic bearing capacities of shallow strip footings

The node-based smoothed finite element method(NS-FEM)is shortly presented for calculations of the static and seismic bearing capacities of shallow strip footings.A series of computations has been performed to assess variations in seismic bearing capacity factors with both horizontal and vertical seismic accelerations.Numerical results obtained agree very well with those using the slip-line method,revealing that the magnitude of the seismic bearing capacity is highly dependent upon the combinations of various directions of both components of the seismic acceleration.An upward vertical seismic acceleration reduces the seismic bearing capacity compared to the downward vertical seismic acceleration in calculations.In addition,particular emphasis is placed on a separate estimation of the effects of soil and superstructure inertia on each seismic bearing capacity component.While the effect of inertia forces arising in the soil on the seismic bearing capacity is non-trivial,and the superstructure inertia is the major contributor to reductions in the seismic bearing capacity.Both tables and charts are given for practical application to the seismic design of the foundations.

Implementing the Node Based Smoothed Finite Element Method as User Element in Abaqus for Linear and Nonlinear Elasticity

In this paper,the node based smoothed-strain Abaqus user element(UEL)in the framework of finite element method is introduced.The basic idea behind of the node based smoothed finite element(NSFEM)is that finite element cells are divided into subcells and subcells construct the smoothing domain associated with each node of a finite element cell[Liu,Dai and Nguyen-Thoi(2007)].Therefore,the numerical integration is globally performed over smoothing domains.It is demonstrated that the proposed UEL retains all the advantages of the NSFEM,i.e.,upper bound solution,overly soft stiffness and free from locking in compressible and nearly-incompressible media.In this work,the constant strain triangular(CST)elements are used to construct node based smoothing domains,since any complex two dimensional domains can be discretized using CST elements.This additional challenge is successfully addressed in this paper.The efficacy and robustness of the proposed work is obtained by several benchmark problems in both linear and nonlinear elasticity.The developed UEL and the associated files can be downloaded from https://github.com/nsundar/NSFEM.

A Smoothing Penalty Function Method for the Constrained Optimization Problem

In this paper, an approximate smoothing approach to the non-differentiable exact penalty function is proposed for the constrained optimization problem. A simple smoothed penalty algorithm is given, and its convergence is discussed. A practical algorithm to compute approximate optimal solution is given as well as computational experiments to demonstrate its efficiency.

Coupling of discrete-element method and smoothed particle hydrodynamics for liquid-solid flows

Particle based methods can be used for both the simulations of solid and fluid phases in multiphase medium, such as the discrete-element method for solid phase and the smoothed particle hydrodynamics for fluid phase. This paper presents a computational method combining these two methods for solid-liquid medium. The two phases are coupled by using an improved model from a reported Lagrangian-Eulerian method. The technique is verified by simulating liquid-solid flows in a two-dimensional lid-driven cavity.

GLOBAL LINEAR AND QUADRATIC ONE-STEP SMOOTHING NEWTON METHOD FOR VERTICAL LINEAR COMPLEMENTARITY PROBLEMS

A one_step smoothing Newton method is proposed for solving the vertical linear complementarity problem based on the so_called aggregation function. The proposed algorithm has the following good features: (ⅰ) It solves only one linear system of equations and does only one line search at each iteration; (ⅱ) It is well_defined for the vertical linear complementarity problem with vertical block P 0 matrix and any accumulation point of iteration sequence is its solution.Moreover, the iteration sequence is bounded for the vertical linear complementarity problem with vertical block P 0+R 0 matrix; (ⅲ) It has both global linear and local quadratic convergence without strict complementarity. Many existing smoothing Newton methods do not have the property (ⅲ).

The Smoothing Newton Method for Solving the Extended Linear Complementarity Problem

The extended linear complementarity problem(denoted by ELCP) can be reformulated as the solution of a nonsmooth system of equations. By the symmetrically perturbed CHKS smoothing function, the ELCP is approximated by a family of parameterized smooth equations. A one-step smoothing Newton method is designed for solving the ELCP. The proposed algorithm is proved to be globally convergent under suitable assumptions.

Smoothing Inexact Newton Method for Solving P_0-NCP Problems

Based on a smoothing symmetric disturbance FB-function,a smoothing inexact Newton method for solving the nonlinear complementarity problem with P0-function was proposed.It was proved that under mild conditions,the given algorithm performed global and superlinear convergence without strict complementarity.For the same linear complementarity problem(LCP),the algorithm needs similar iteration times to the literature.However,its accuracy is improved by at least 4 orders with calculation time reduced by almost 50%,and the iterative number is insensitive to the size of the LCP.Moreover,fewer iterations and shorter time are required for solving the problem by using inexact Newton methods for different initial points.

Bubble-Enriched Smoothed Finite Element Methods for Nearly-Incompressible Solids

This work presents a locking-free smoothed finite element method(S-FEM)for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity.The proposed method overcomes well-known issues of standard finite element methods(FEM)in the incompressible limit:the over-estimation of stiffness and sensitivity to severely distorted meshes.The concepts of cell-based,edge-based and node-based S-FEMs are extended in this paper to three-dimensions.Additionally,a cubic bubble function is utilized to improve accuracy and stability.For the bubble function,an additional displacement degree of freedom is added at the centroid of the element.Several numerical studies are performed demonstrating the stability and validity of the proposed approach.The obtained results are compared with standard FEM and with analytical solutions to show the effectiveness of the method.

Adaptive Smoothing Method Based on Fuzzy Theory Study and Realization

In this paper, we study about a method to optimize the fused track quality in intelligence network of radar target fusion system, considering the role of people in the fusion system;we start to find ways to optimize the quality of the fused track, and adaptive smoothing method is proposed based on fuzzy theory. Tests show that this method can greatly improve the quality of the fused track system for battlefield reconnaissance provides high-quality, high-reliability battlefield.

A Cell-Based Linear Smoothed Finite Element Method for Polygonal Topology Optimization

The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.

A Smoothed Finite Element Method for the Static and Free Vibration Analysis of Shells

A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples.

An Enhanced Steepest Descent Method for Global Optimization-Based Mesh Smoothing

In order to speed up the global optimization-based mesh smoothing, an enhanced steepest descent method is presented in the paper. Numerical experiment results show that the method performs better than the steepest descent method in the global smoothing. We also presented a physically-based interpretation to explain why the method works better than the steepest descent method.

A Class of Smoothing Modulus-Based Iterative Method for Solving Implicit Complementarity Problems

In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point equation, then introduces a smoothing function to obtain its approximation solutions. The convergence analysis of the algorithm was given, and the efficiency of the algorithms was verified by numerical experiments.

Almost Sure Convergence of Proximal Stochastic Accelerated Gradient Methods

Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.

SMOOTHING NEWTON ALGORITHM FOR THE CIRCULAR CONE PROGRAMMING WITH A NONMONOTONE LINE SEARCH

In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.

A novel twice-interpolation finite element method for solid mechanics problems

Formulation and numerical evaluation of a novel twice-interpolation finite element method （TFEM） is presented for solid mechanics problems. In this method, the trial function for Galerkin weak form is constructed through two stages of consecutive interpolation. The primary interpolation follows exactly the same procedure of standard FEM and is further reproduced according to both nodal values and averaged nodal gradients obtained from primary interpolation. The trial functions thus constructed have continuous nodal gradients and contain higher order polynomial without increasing total freedoms. Several benchmark examples and a real dam problem are used to examine the TFEM in terms of accuracy and convergence. Compared with standard FEM, TFEM can achieve significantly better accuracy and higher convergence rate, and the continuous nodal stress can be obtained without any smoothing operation. It is also found that TFEM is insensitive to the quality of the elemental mesh. In addition, the present TFEM can treat the incompressible material without any modification.

Optimization of buckling load for laminated composite plates using adaptive Kriging-improved PSO:A novel hybrid intelligent method

An effective hybrid optimization method is proposed by integrating an adaptive Kriging(A-Kriging)into an improved partial swarm optimization algorithm(IPSO)to give a so-called A-Kriging-IPSO for maximizing the buckling load of laminated composite plates(LCPs)under uniaxial and biaxial compressions.In this method,a novel iterative adaptive Kriging model,which is structured using two training sample sets as active and adaptive points,is utilized to directly predict the buckling load of the LCPs and to improve the efficiency of the optimization process.The active points are selected from the initial data set while the adaptive points are generated using the radial random-based convex samples.The cell-based smoothed discrete shear gap method(CS-DSG3)is employed to analyze the buckling behavior of the LCPs to provide the response of adaptive and input data sets.The buckling load of the LCPs is maximized by utilizing the IPSO algorithm.To demonstrate the efficiency and accuracy of the proposed methodology,the LCPs with different layers(2,3,4,and 10 layers),boundary conditions,aspect ratios and load patterns(biaxial and uniaxial loads)are investigated.The results obtained by proposed method are in good agreement with the literature results,but with less computational burden.By applying adaptive radial Kriging model,the accurate optimal resultsebased predictions of the buckling load are obtained for the studied LCPs.