Robust projection method for Fredholm integral equation of the second kind

The projection method based on the Schauder basis expansion for solving the Fredholm integral equation of the second kind is investigated. (1) It is shown that any given finite linearly independent function set in L ^p [0, 1] can be extended as a Schauder basis. The truncation of the dual Schauder bases is then used to form the projection in approximating the kernel. (2) With the finite rank approximation, the use of the Sherman–Morrison–Woodbury formula achieves efficient implementation. The computation is successive when dimension of projection space increases. Numerical experiments demonstrate the robustness of the Schauder basis expansion.     

A weighted H1 seminorm regularization method for Fredholm integral equations of the first kind

Many problems in mathematics and engineering lead to Fredholm integral equations of the first kind, e.g. signal and image processing. These kinds of equations are difficult to solve numerically since they are ill-posed. Therefore, regularization is required to obtain a reasonable approximate solution. This paper presents a new regularization method based on a weighted H¹ seminorm. Details of numerical implementation are given. Numerical examples, including one-dimensional and two-dimensional integral equations, are presented to illustrate the efficiency of the proposed approach. Numerical results show that the proposed regularization method can restore edges as well as details.     

High-accuracy quadrature methods for solving boundary integral equations of steady-state anisotropic heat conduction problems with Dirichlet conditions

This paper presents the mechanical quadrature methods (MQMs) for solving the boundary integral equations of steady-state anisotropic heat conduction equation on the smooth domains and polygons, respectively. The costless and high-accurate Sidi–Israeli quadrature formula are applied to deal with the integrals in which the kernels have a logarithmic singularity. Especially, the Sidi transformation is used for the polygon cases in order to obtain a rapid convergence by degrading the singularity at the corners on the boundary. The convergence and stability of the MQMs solution are proved based on Anselone's collective compact theory. In addition, asymptotic error expansion of the MQMs shows that the approximation order is of O(h³), where h is the partition size of the boundary. Finally, numerical examples are tested and results verify the theoretical analysis.     

广义分层混合模糊系统及其泛逼近性

为避免广义模糊系统出现规则爆炸现象, 引进实参数将Mamdani模糊系统和T--S模糊系统统一起来建立广义分层混合模糊系统, 进而给出了广义分层混合模糊系统的数学表示. 此外, 应用方形分片线性函数的优良性质获得该广义分层混合模糊系统在积分模意义下仍具有泛逼近性, 并通过实例及仿真说明该分层混合模糊系统能够避免模糊规则爆炸问题.     

一类不确定离散时间系统的积分滑模控制

针对一类同时存在匹配和非匹配不确定性的离散时间系统,提出一种基于幂次函数的离散积分滑模控制方法.理论分析表明,所提出的方法可以消除离散积分滑模控制系统的抖振,而且能够保证对系统的匹配和非匹配不确定性具有强鲁棒性.在系统不确定性的界未知的情况下,通过引入一步延时干扰估计完成了控制器的设计,并给出了闭环系统稳定性证明.仿真结果验证了所提出方法的有效性.     

Aggregating multiple classification results using Choquet integral for financial distress early warning

Financial distress prediction methods based on combination classifier become a rising trend in this field. This paper applies Choquet integral to ensemble single classifiers and proposes a Choquet integral-based combination classifier for financial distress early warning. Also, as the conditions between training and pattern recognition cannot be completely consistent, so this paper proposes an adaptive fuzzy measure by using the dynamic information in the single classifier pattern recognition results which is more reasonable than the static prior fuzzy density. Finally, a comparative analysis based on Chinese listed companies’ real data is conducted to verify prediction accuracy and stability of the combination classifier. The experiment results indicate that financial distress prediction using Choquet integral-based combination classifier has higher average accuracy and stability than single classifiers.     

色选机喂料器振幅和产量控制的研究

提出了一种喂料器振幅闭环控制方案,利用霍尔传感器作为反馈器件,采用积分控制算法,使喂料器的振幅在线动态调节并自适应振动环境的变化,达到振幅稳定。经实验证明,这种方法能有效地改善原喂料器振幅不稳和产量不稳的问题,为色选机喂料器振幅控制提供了一种新的解决方案。     

大型风力发电叶片变形的摄像测量方法研究

将摄像测量方法应用于大型风力发电叶片力学实验的变形测量中.叶片在发生大幅度整体变形的同时发生微小的屈曲变形,这给测量带来了很多问题,为此提出并联式组网测量的方法.固定像机大视场远距离交会测量整体变形;相对固定的立体像机小视场近距离交会测量叶片上每个长约3m的局部段的屈曲变形,并且跟随叶片上待测量区域移动.所有像机并联式组网,同步触发.测量过程中的关键技术还有像机标定和畸变校正、格网点和黑白标志块的高精度半自动提取、坐标系的统一等.实验结果表明:整体变形的测量精度优于0.5mm,屈曲变形中网格点三维坐标的测量精度优于0.1mm;系统搭建相对简便、测量内容丰富、范围广、精度高、且能供事后处理和分析.     

On the use of a spectrum-based model for linear viscoelastic materials

A new spectrum-based model for describing the behavior of time-dependent materials is presented. In this paper, unlike most prior modeling techniques, the time-dependent response of viscoelastic materials is not expressed through the use of series. Instead, certain criteria have been imposed to select a spectrum function that has the potential of describing a wide range of material behavior. Another consequence of choosing the spectrum function of the type used in this paper is to have a few closed form analytic solutions in the theory of linear viscoelasticity. The Laplace transform technique is used to obtain the necessary formulae for viscoelastic Lame' functions, relaxation and bulk moduli, creep bulk and shear compliance, as well as Poisson's ratio. By using the Elastic–Viscoelastic Correspondence Principle (EVCP), material constants appearing in the proposed model are obtained by comparing the experimental data with the solution of the integral equation for a simple tensile test. The resulting viscoelastic functions describe the material properties which can then be used to express the behavior of a material in other loading configurations. The model's potential is demonstrated and its limitations are discussed.     

Thermal explosion in a hot gas mixture with organic gel fuel droplets

Recent experimental evidence has uncovered the peculiar behavior of certain gel droplets which, under appropriate ambient thermal conditions, evaporate and burn in an oscillatory fashion. In this work a preliminary foray is made into the theoretical analysis of the nature of the evolution of a hot gas mixture containing organic gel fuel droplets with oscillatory evaporation within the context of thermal-explosion theory. The problem is modeled as a system of highly nonlinear singularly perturbed ordinary differential equations. Non-dimensionalization of the equations enables identification of the parameters that play a major role in determining the dynamical regimes of the system of equations. The method of integral manifolds is exploited for the analysis and it is found, that for certain parametric regions, the system exhibits new dynamical behavior that is quite different from that found for conventional liquid droplets.