Fuzzy smooth support vector machine with different smooth functions

Smooth support vector machine （SSVM） changs the normal support vector machine （SVM） into the unconstrained op- timization by using the smooth sigmoid function. The method can be solved under the Broyden-Fletcher-Goldfarb-Shanno （BFGS） algorithm and the Newdon-Armijio （NA） algorithm easily, however the accuracy of sigmoid function is not as good as that of polyno- mial smooth function. Furthermore, the method cannot reduce the influence of outliers or noise in dataset. A fuzzy smooth support vector machine （FSSVM） with fuzzy membership and polynomial smooth functions is introduced into the SVM. The fuzzy member- ship considers the contribution rate of each sample to the optimal separating hyperplane and makes the optimization problem more accurate at the inflection point. Those changes play a positive role on trials. The results of the experiments show that those FSSVMs can obtain a better accuracy and consume the shorter time than SSVM and lagrange support vector machine （LSVM）.

EXTENSION OF SMOOTHING FUNCTIONS TO SYMMETRIC CONE COMPLEMENTARITY PROBLEMS

The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity problems. Computable formulas for these functions and their Jacobians are derived. In addition, it is shown that these functions are Lipschitz continuous with respect to parameter # and continuously differentiable on J × J for any μ 〉 0.

Template-based smoothing functions for data smoothing in Geodesy

This paper is aimed at the derivation of a discrete data smoothing function for the discrete Dirichlet condition in a regular grid on the surface of a spheroid.The method employed here is the local L^2-seminorm minimization,through Euler-Lagrange method,for the Beltrami operator.The method results in a weighted average of the surrounding points in a te mplate based on the first order Taylor expansion of the unknown function under consideration.The coefficients of the weighted average are calculated and used to smooth the Geoid height data in Iran,derived from the EGM2008 geopotential model.

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.

OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS(1)

In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.

New smooth gap function for box constrained variational inequalities

A new smooth gap function for the box constrained variational inequality problem （VIP） is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.

A NEW FORMULATION OF BERNSTEIN-BEZIER BASED SMOOTHNESS CONDITIONS FOR pp FUNCTIONS

In this note, we establish a new formulation of smoothness conditions for piecewise polynomial (: =pp) functions in terms of the B-net representation in the general n-dimensional setting. It plays an important role for 2-dimensional setting in the constructive proof of the fact that the spaces of polynomial splines with smoothness rand total degree k≥3r+2 over arbitrary triangulations achieve the optimal approximation order with the approximation constant depending only on k and the smallest angle of the partition in [5].

Solving frictional contact problems by two aggregate-function-based algorithms

Three dimensional frictional contact problems are formulated as linear complementarity problems based on the parametric variational principle. Two aggregate-functionbased algorithms for solving complementarity problems are proposed. One is called the self-adjusting interior point algorithm, the other is called the aggregate function smoothing algorithm. Numerical experiment shows the efficiency of the proposed two algorithms.

Modulation recognition of communication signals based on SCHKS-SSVM

A novel modulation recognition algorithm is proposed by introducing a Chen-Harker-Kanzow-Smale (CHKS) smooth function into the C-support vector machine deformation algorithm. A set of seven characteristic parameters is selected from a range of parameters of communication signals including instantaneous amplitude, phase, and frequency. And the Newton-Armijo algorithm is utilized to train the proposed algorithm, namely, smooth CHKS smooth support vector machine (SCHKS-SSVM). Compared with the existing algorithms, the proposed algorithm not only solves the non-differentiable problem of the second order objective function, but also reduces the recognition error. It significantly improves the training speed and also saves a large amount of storage space through large-scale sorting problems. The simulation results show that the recognition rate of the algorithm can batch training. Therefore, the proposed algorithm is suitable for solving the problem of high dimension and its recognition can exceed 95% when the signal-to-noise ratio is no less than 10 dB.

New family of piecewise smooth support vector machine

Support vector machines （SVMs） have been extensively studied and have shown remarkable success in many applications. A new family of twice continuously differentiable piecewise smooth functions are used to smooth the objective function of uncon- strained SVMs. The three-order piecewise smooth support vector machine （TPWSSVMd） is proposed. The piecewise functions can get higher and higher approximation accuracy as required with the increase of parameter d. The global convergence proof of TPWSSVMd is given with the rough set theory. TPWSSVMd can efficiently handle large scale and high dimensional problems. Nu- merical results demonstrate TPWSSVMa has better classification performance and learning efficiency than other competitive base- lines.

Sliding mode control for mobile welding robot

The sliding mode controller of mobile welding robot is established in this paper through applying the method of variable structure control with sliding mode into the control of the mobile welding robot. The traditional switching function smooth method is improved by combining the smoothed switching function with the time-varying control gain. It is shown that the proposed sliding mode controller is robust to bounded external disturbances. Experimental results demonstrate that sliding mode controller algorithm can be used into seam tracking and the tracking system is stable with bounded uncertain disturbance. In the seam tracking process, the robot moves steadily without any obvious chattering.

Solving Smooth Generalized Equations Using Modified Gauss-Type Proximal Point Method

Consider X and Y are two real or complex Banach spaces. We introduce and study a modified Gauss-type proximal point algorithm (in short modified G-PPA) for solving the generalized equations of the form 0 ∈h(x) + H(x), where h : X → Y is a smooth function on Ω ⊆X and H : X ⇉2Y is a set valued mapping with closed graph. When H is metrically regular and under some sufficient conditions, we analyze both semi-local and local convergence of the modified G-PPA. Moreover, the convergence results of the modified G-PPA are justified by presenting a numerical example.

Rational Characterization Complex Geology Model——Macro Velocity Model

The accuracy of migration velocity construction is always a key problem of the image quality of pre-stack depth migration. The velocity model construction process is a process from an unknown to unknown iteration procedure and involves three important steps — model building, migration and model modification. It is necessary to rationally describe the velocity model, according to the complexity of the problem. Taking the Marmousi model as a study object, We established some standards for a rational description of the velocity model on the basis of different velocity space scales, analysis varieties of travel time, and image quality. It is considered that for any given seismic data gathered in the migration velocity model the space wavelength of velocity, which should be expressed in variation of space wavelength of various frequency contents, appears in the seismic data. Some space wavelengths, which are necessary for a description of the model velocity field, are also varying with the layer complexity. For a simple layer velocity structure it is sufficient to apply a simple velocity model (the space wavelength is large enough), whereas, for a complicated layer velocity structure it is necessary to take a velocity model of a more precise scale. In fact, when we establish a velocity model, it is difficult to describe the velocity model at a full space scale, so it is important to limit the space scale of the velocity model according to the complexity of a layer structure and establish a rational macro velocity model.

Two-dimensional finite element mesh generation algorithm for electromagnetic field calculation

Two-dimensional finite element mesh generation algorithm for electromagnetic field calculation is proposed in this paper to improve the efficiency and accuracy of electromagnetic calculation. An image boundary extraction algorithm is developed to map the image on the geometric domain. Identification algorithm for the location of nodes in polygon area is proposed to determine the state of the node. To promote the average quality of the mesh and the efficiency of mesh generation, a novel force-based mesh smoothing algorithm is proposed. One test case and a typical electromagnetic calculation are used to testify the effectiveness and efficiency of the proposed algorithm. The results demonstrate that the proposed algorithm can produce a high-quality mesh with less iteration.

Simulation of Oil-Water Flow in Shale Oil Reservoirs Based on Smooth Particle Hydrodynamics

A Smooth Particle Hydrodynamics(SPH)method is employed to simulate the two-phase flow of oil and water in a reservoir.It is shown that,in comparison to the classical finite difference approach,this method is more stable and effective at capturing the complex evolution of this category of two-phase flows.The influence of several smooth functions is explored and it is concluded that the Gaussian function is the best one.After 200 days,the block water cutoff for the Gaussian function is 0.3,whereas the other functions have a block water cutoff of 0.8.The effect of various injection ratios on real reservoir production is explored.When 14 and 8 m^(3)/day is employed,the water breakthrough time is 130 and 170 days,respectively,and the block produces 9246 m^(3) and 6338 m^(3) of oil cumulatively over 400 days.

APPROXIMATION PROPERTIES OF LAGRANGE INTERPOLATION POLYNOMIAL BASED ON THE ZEROS OF (1-x^2)cosnarccosx

We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.

某些周期函数类的N宽度

This paper considers the Kolmogorov width,the Gelfand width and the Linear width of the periodic smooth functions with boundary conditions in Orlicz space.Further,the relationships among these three types of width are obtained.

An Efficient Smooth Quantile Boost Algorithm for Binary Classification

In this paper, we propose a Smooth Quantile Boost Classification (SQBC) algorithm for binary classification problem. The SQBC algorithm directly uses a smooth function to approximate the “check function” of the quantile regression. Compared to other boost-based classification algorithms, the proposed algorithm is more accurate, flexible and robust to noisy predictors. Furthermore, the SQBC algorithm also can work well in high dimensional space. Extensive numerical experiments show that our proposed method has better performance on randomly simulations and real data.

GENERALIZED BESOV SPACES AND TRIEBEL-LIZORKIN SPACES

In this paper the classical Besov spaces B^sp.q and Triebel-Lizorkin spaces F^sp.q for s∈R are generalized in an isotropy way with the smoothness weights { ｜2j｜^α→ln }7=0. These generalized Besov spaces and Triebel-Lizorkin spaces, denoted by B^α→p.q and F^α→p.q for α^→ E Nk and k ∈N, respectively, keep many interesting properties, such as embedding theorems （with scales property for all smoothness weights）, lifting properties for all parameters 5, and duality for index 0 〈 p 〈∞ By constructing an example, it is shown that there are infinitely many generalized Besov spaces and generalized Triebel-Lizorkin spaces lying between B^sp.q and ∪t〉s B^tp.q, and between F^sp.q and ∪t〉s F^tp.q, respectively.

FURTHER STUDY ON A DUAL ALGORITHM

The dual algorithm for minimax problems is further studied in this paper.The resulting theoretical analysis shows that the condition number of the corresponding Hessian of the smooth modified Lagrange function with changing parameter in the dual algorithm is proportional to the reciprocal of the parameter,which is very important for the efficiency of the dual algorithm.At last,the numerical experiments are reported to validate the analysis results.