基于三次样条插值的支持向量机研究

在传统支持向量机的分类求解算法中,严格凸的无约束最优化问题中单变量函数X+是不可微的,三次样条插值多项式光滑的支持向量机模型采用的是一种多项式光滑技术,使用三次样条插值二次多项式来逼近单变量函数O+,将原始非光滑的支持向量机模型转化为光滑模型,从而可以使用最常用的最优化的算法进行求解,给出了使用三次样条插值方法来光滑单变量函数的具体推导过程.使用UCI机器学习数据集中的数据,通过实验验证了该模型的有效性.     

需求分布不确定条件下的多周期库存鲁棒优化模型

在离散需求情景概率不确定的条件下, 建立基于最大最小方法的多周期库存鲁棒优化模型. 考虑需求分布分别隶属于区间和椭球不确定集两种情形, 运用对偶理论将多周期库存鲁棒优化模型转化为易于求解的凸规划问题. 数值结果表明, 与已知需求分布下的系统最优绩效相比, 采用鲁棒订货策略虽然会导致部分绩效损失, 但损失值很小, 表明基于鲁棒优化的多周期库存订货策略具有良好的鲁棒性, 能够有效抑制需求分布不确定性对库存运作绩效的影响.

     

一类不确定性系统的鲁棒正实性分析与综合

考虑一类具有多项式型不确定性系统的鲁棒正实性分析和综合问题。这类不确定模型是区间摄动和范数有界摄动系统的自然推广。给出了一个系统具有鲁棒扩展严格正实性 (ESPR)的充分条件 ,利用该条件可估计出使系统保持 ESPR的最大参数摄动范围。在 ESPR分析的基础上 ,进一步给出了ESPR控制器的存在条件和控制器的构造方法。通过凸优化算法 ,得到了所提出方法意义下具有最大摄动界的 ESPR控制器设计方法。     

期望指标下一类线性周期系统鲁棒状态估计

针对满足多重区域指标约束的鲁棒滤波问题 ,以离散线性周期系统为研究对象 ,利用周期系统参数在某区间变化的特性 ,将周期系统满足极点或极点 /协方差指标的估计问题转化为区间系统的鲁棒估计问题。采用线性矩阵不等式 (L MIs)法进行凸优化 ,求解对应区间系统的满意估计增益 ,并设计相应鲁棒状态估计器。数值算例验证了相关的结论。     

基于改进HBA算法的生鲜闭环供应链网络鲁棒优化设计

针对生鲜闭环供应链网络设计问题,建立了一种基于生鲜闭环供应链网络的鲁棒优化模型,以解决供应链网络中的不确定性问题。首先,针对涵盖五个节点的生鲜供应链网络结构建立了多周期、多产品,以最小化成本、最小环境影响为目标的混合整数规划模型,采用模糊折中规划与区间数据鲁棒优化方法进行处理;其次,在原有蜜獾算法的基础上引入差分进化原则,增强算法的全局搜索能力与收敛速度;最后,通过MATLAB数值分析与仿真实例表明,所提鲁棒优化模型与蜜獾算法在求解生鲜闭环供应链网络设计问题中具有明显优势。     

多形状参数的二次非均匀双曲B-样条曲线

给出了一类带多个形状参数的二次非均匀双曲B-样条曲线,这类曲线具有二次多项式B-样条曲线的许多重要性质.根据形状参数的不同取值,能整体或局部地调控曲线的形状;无需重节点技术或解线性方程组,就能使曲线直接插值于某些控制点或控制边.此外,这类曲线能精确地表示双曲线.     

一类推广的两步鲁棒辨识算法

基于传统的两步辨识方法，提出一类当频域数据样本在系统频率段上非均匀分布时的H∞鲁棒辨识方法，分析了相应的最差情况的辨识误差，并给出了采用Lidstone插值样条算子和三角窗函数时显式最差情况辨识误差上界。     

多层积分值三次样条拟插值

目的 在实际问题中,某些插值问题结点处的函数值往往是未知的,而仅仅知道一些连续等距区间上的积分值。为此提出了一种基于未知函数在连续等距区间上的积分值和多层样条拟插值技术来解决函数重构。该方法称之为多层积分值三次样条拟插值方法。方法 首先,利用积分值的线性组合来逼近结点处的函数值;然后,利用传统的三次B-样条拟插值和相应的误差函数来实现多层三次样条拟插值;最后,给出两层积分值三次样条拟插值算子的多项式再生性和误差估计。结果 选取无穷次可微函数对多层积分值三次样条拟插值方法和已有的积分值三次样条拟插值方法进行对比分析。数值实验印证了本文方法在逼近误差和数值收敛阶均稍占优。结论本文多层三次样条拟插值函数能够在整体上很好的逼近原始函数,一阶和二阶导函数。本文方法较之于已有的积分值三次样条拟插值方法具有更好的逼近误差和数值收敛阶。该方法对连续等距区间上积分值的函数重构具有普适性。     

变采样周期和数据包随机丢失的NCS鲁棒H∞ SymboleB控制

网络控制系统与传统的点对点控制方式不同,数据传输具有时延和随机丢包,且为了对信息资源进行合理的分配和调度常采用时变采样方式.本文首先给出NCS的离散区间动态模型,该模型以Bernoulli分布序列描述NCS数据丢包的随机性,并以不确定区间矩阵描述NCS的采样周期与传输时延的时变性;在此基础上,基于线性矩阵不等式（LMI）技术,给出具有时变有界采样周期和数据随机丢包NCS的鲁棒H∞控制器存在充分条件,且将控制器的求解问题转化为一个有限维LMI凸优化问题,便于数值计算.所设计的控制器可以保证系统渐近稳定且具有一定的H∞扰动抑制水平γ.数值仿真表明提出控制器设计方法的有效性。     

一族三次样条光滑半监督支持向量机

针对半监督支持向量分类优化中的非凸非光滑化问题,建立光滑半监督支持向量机模型,提出基于分段多项式函数和插值思想构造一个新的三次样条光滑函数,从而可以更好地逼近对半监督支持向量机中非光滑的对称铰链损失函数部分,构造出基于此光滑函数的具有二阶光滑的半监督支持向量机模型。进而可以用优化中的光滑算法来求解该模型,并分析所构造的三次样条函数对对称铰链损失函数的逼近精度。通过数据实验证明所构造的新的光滑半监督模型具有较好的分类效果和效率。     

The Unstructured Mesh Finite Element Method for the Two-Dimensional Multi-term Time–Space Fractional Diffusion-Wave Equation on an Irregular Convex Domain

In this paper, the two-dimensional multi-term time-space fractional diffusion-wave equation on an irregular convex domain is considered as a much more general case for wider applications in fluid mechanics. A novel unstructured mesh finite element method is proposed for the considered equation. In most existing works, the finite element method is applied on regular domains using uniform meshes. The case of irregular convex domains, which would require subdivision using unstructured meshes, is mostly still open. Furthermore, the orders of the multi-term time-fractional derivatives have been considered to belong to (0, 1] or (1, 2] separately in existing models. In this paper, we consider two-dimensional multi-term time-space fractional diffusion-wave equations with the time fractional orders belonging to the whole interval (0, 2) on an irregular convex domain. We propose to use a mixed difference scheme in time and an unstructured mesh finite element method in space. Detailed implementation and the stability and convergence analyses of the proposed numerical scheme are given. Numerical examples are conducted to evaluate the theoretical analysis.     

B-样条曲面的保凸拼接

利用参数曲面局部凸的条件,导出了(准)均匀B-样条曲面局部凸的充分条件。证明了带有凸的平行四边形控制子网格的(准)均匀B-样条曲面片的凸的。给出了(准)均匀B-样条曲面保凸拼接的控制顶点算法,并给出了几个三次B-样条曲面保凸拼接实例。     

Robust power allocation algorithm for analog network coding with imperfect CSI

Power allocation promises significant benefits in wireless networks. However, these benefits depend on knowledge of the channel state information （CSI）, which is hardly perfect. Therefore, robust algorithms that take into account such CSI uncertainties play an important role in the design of practical systems. In this paper, we formulate the power allocation problem as the maximum individual outage probability minimization subject to total power consumption for analog network coding （ANC） protocol of a two-way relay system. We show that these problems can be cast as convex optimization problems. Non-robust power allocation algorithm is first developed under the ideal assumption of perfect CSI. Then we introduce robust optimization methodology that accounts for the imperfect CSI. We show that ignoring CSI uncertainties in our designs can lead to drastic performance degradation. On the other hand, the proposed robust power allocation provides significant performance gain over non-robust power allocation and uniform power allocation in terms of overall system outage probability over a wide range of channel estimation errors. This work highlights the importance of the proposed robust algorithm in realistic two-way relaying networks.     

Statistic PID tracking control for non-Gaussian stochastic systems based on T-S fuzzy model

A new robust proportional-integral-derivative （PID） tracking control framework is considered for stochastic systems with non-Gaussian variable based on B-spline neural network approximation and T-S fuzzy model identification. The tracked object is the statistical information of a given target probability density function （PDF）, rather than a deterministic signal. Following B-spline approximation to the integrated performance function, the concerned problem is transferred into the tracking of given weights. Different from the previous related works, the time delay T-S fuzzy models with the exogenous disturbances are applied to identify the nonlinear weighting dynamics. Meanwhile, the generalized PID controller structure and the improved convex linear matrix inequalities （LMI） algorithms are proposed to fulfil the tracking problem. Furthermore, in order to enhance the robust performance, the peak-to-peak measure index is applied to optimize the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.     

一种求解线性控制系统可达集的数值方法

针对线性控制系统,研究应用常微分方程数值方法和优化技术相结合的近似可达集的方法.首先,用常微分方程数值方法对系统进行离散化.然后,提出基于优化技术的外部投影法来近似离散系统的可达集.外部投影法构造有限多个投影问题,每个都对应一个凸优化问题,通过求解这些凸优化问题最终可以得到可达集的近似描述.最后,通过数值仿真结果验证了所提出方法的有效性.与文献中已有的方法相比,在求解相同数量凸优化问题的情况下,外部投影法的近似精度更高.     

Integration of topology and shape optimization for design of structural components

This paper presents an integrated approach that supports the topology optimization and CAD-based shape optimization. The main contribution of the paper is using the geometric reconstruction technique that is mathematically sound and error bounded for creating solid models of the topologically optimized structures with smooth geometric boundary. This geometric reconstruction method extends the integration to 3-D applications. In addition, commercial Computer-Aided Design (CAD), finite element analysis (FEA), optimization, and application software tools are incorporated to support the integrated optimization process. The integration is carried out by first converting the geometry of the topologically optimized structure into smooth and parametric B-spline curves and surfaces. The B-spline curves and surfaces are then imported into a parametric CAD environment to build solid models of the structure. The control point movements of the B-spline curves or surfaces are defined as design variables for shape optimization, in which CAD-based design velocity field computations, design sensitivity analysis (DSA), and nonlinear programming are performed. Both 2-D plane stress and 3-D solid examples are presented to demonstrate the proposed approach. Received January 27, 2000 Communicated by J. Sobieski     

Algorithms for unconstrained global optimization of nonlinear (polynomial) programming problems: The single and multi-segment polynomial B-spline approach

We investigate the use of the polynomial B-spline form for unconstrained global optimization of multivariate polynomial nonlinear programming problems. We use the B-spline form for higher order approximation of multivariate polynomials. We first propose a basic algorithm for global optimization that uses several accelerating algorithms such as cut-off test and monotonicity test. We then propose an improved algorithm consisting of several additional ingredients, such as a new subdivision point selection rule and a modified subdivision direction selection rule. The performances of the proposed basic and improved algorithms are tested and compared on a set of 14 test problems under two test conditions. The results of the tests show the superiority of the improved algorithm with multi-segment B-spline over that of the single segment B-spline, in terms of the chosen performance metrics. We also compare the quality of the set of all global minimizers found using the proposed algorithms (basic & improved) with those using well-known solvers BARON and Gloptipoly, on a smaller set of four test problems. The problems in the latter set have multiple global minimizers. The results show the superiority of the proposed algorithms, in that they are able to capture all the global minimizers, whereas Gloptipoly and BARON fail to do so in some of the test problems.     

混合B样条实体模型的等几何拓扑优化

等几何拓扑优化方法将经典拓扑优化理论中的有限元分析过程更改为等几何分析计算,从而提 高了拓扑优化的效率与稳定性。针对现有的等几何拓扑优化方法在处理复杂实体结构优化问题时具有一定的局 限性,提出一种非结构化样条实体等几何拓扑优化方法。基于混合 B 样条构造技术,在非结构化六面体网格上 构造具有复杂结构的样条实体,并将其作为拓扑优化问题的设计域。用于描述这一样条实体的基函数被直接应 用于材料密度分布的表达以及等几何分析计算。在数值算例中,该方法表现出应用于复杂结构时的良好稳定性 和鲁棒性。研究成果对等几何拓扑优化方法应用于实际工程问题具有一定的参考意义。     

Interval fuzzy modeling applied to Wiener models with uncertainties.

This correspondence addresses the problem of interval fuzzy model identification and its use in the case of the robust Wiener model. The method combines a fuzzy identification methodology with some ideas from linear programming theory. On a finite set of measured data, an optimality criterion which minimizes the maximum estimation error between the data and the proposed fuzzy model output is used. The min-max optimization problem can then be seen as a linear programming problem that is solved to estimate the parameters of the fuzzy model in each fuzzy domain. This results in lower and upper fuzzy models that define the confidence interval of the observed data. The model is called the interval fuzzy model and is used to approximate the static nonlinearity in the case of the Wiener model with uncertainties. The resulting model has the potential to be used in the areas of robust control and fault detection.