传感器数据的高精度重构方法及其性能研究

不同传感器具有不同的非线性。为提高传感器数据重构精度,本文给出两种数据重构方法。对于不是特别严重的非线性,采用最小二乘拟合与径向基函数残差插值进行融合重构,可以在增加有限计算量条件下提高数据的近似精度;对于非线性较严重的传感器,为兼顾局部特性,采用移动最小二乘法进行数据重构,它通过全局近似向局部近似的转化,同样使重构结果具有满意的近似精度。选用两种不同传感器进行实验,结果表明两种方法均行之有效。     

基于最小二乘RBF的含噪声散乱数据逼近

径向基函数能够有效的对散乱数据进行差值和逼近,因此在信号和图形处理等领域应用广泛,例如信号重构.针对从含有噪音的散乱数据中逼近原始数据,提出了一种基于最小二乘的变分模型,该模型由包含L2范数的拟合项和光滑项构成,光滑项通过三角网格上的拉普拉斯平滑方法来实现对函数梯度的约束,并应用最小二乘法求解该模型.最后通过数值实验对噪音数据进行逼近和误差分析来验证此方法的有效性.     

非线性多功能传感器信号重构的抗差估计方法研究

在非线性多功能传感器的信号重构过程中,训练样本集不可避免地夹杂粗差数据。为了得到既有较强抗差性又有较高效率的估值,采用抗差最小二乘法在粗差干扰条件下进行参数估计。抗差最小二乘估计通过等价权把抗差估计原理与加权最小二乘形式结合在一起,因此在抵抗粗差的同时保持了最小二乘法的优点。非线性信号重构的粗差抑制结果表明,抗差最小二乘法计算速度快,且具有良好的抗粗差能力和收敛可靠性。     

基于移动最小二乘的传感器数据重构

纳米气体传感器的灵敏度易受温度变化的影响.为了有效改善纳米传感器的温度特性,方便确定其最佳工作条件,利用移动最小二乘法对其灵敏度-温度数据进行拟合,并建立相应的近似模型.移动最小二乘法通过紧支性加权的局部近似,使所建模型较常规最小二乘模型更精确、更光滑.实验证实了基于移动最小二乘拟合的近似性能.该方法在传感器数据精确重构领域具有良好的应用前景.     

移动最小二乘代理模型支持域半径的优化方法

移动最小二乘代理模型描述局部波动的能力优于一般的代理模型,但其精度受支持域半径的影响。在经验公式的基础上提出了一种针对移动最小二乘代理模型支持域半径的优化方法。对支持域内抽样点数寻优获取最佳半径值,提高近似精度进而达到减少抽样点的目的。数值实验结果表明,对于不同基函数阶次和权函数的情况,提出的方法大大提高了移动最小二乘代理模型的近似精度,与基于经验公式的移动最小二乘代理模型相比,其仅需较少的抽样点即可达到相同的近似精度。     

面向非匀点云拟合的RSR移动最小二乘法

针对传统的移动最小二乘法在非均匀分布的采样点集拟合中的不足,提出了影响域半径动态调整的移动最小二乘法（RSRMLS）。在传统移动最小二乘法（MLS）的基础上,根据拟合子区域采样点数据稀疏情况,该方法可自动调整MLS的半径区域大小。通过对相同数据点集的拟合比较,提出的RSRMLS拟合效果明显优于传统MLS。     

电容式降雨传感器及其特性曲线拟合方法

针对将电容式传感器应用于降雨测量时,特性曲线的非线性误差较大问题,分别采用最小二乘曲线拟合法和径向基函数(RBF)神经网络对其输出特性曲线进行拟合.结果表明:RBF神经网络模型具有更强的非线性映射能力,其拟合精度明显高于最小二乘多项式模型.     

基于B样条整体最小二乘的非线性多功能传感器信号重构方法

提出一种基于B样条整体最小二乘(Total least squares,TLS)的非线性多功能传感器信号重构新方法.该方法利用B样条基函数直接构建描述多功能传感器传递函数反函数的张量积B样条曲面;采用TLS求解超定方程组以获得稳定的控制系数估计.以二输入二输出多功能传感器模型为实验对象,在两种非线性情况下对多功能传感器的输入信号进行了重构,重构相对误差分别为0.162％和1.043％,并与常用重构方法进行了对比分析.理论和实验表明,B样条TLS重构方法对非线性多功能传感器传递函数的反函数具有良好的逼近性能,在信号重构中表现出较好的有效性.     

基于移动最小二乘法的气动力数据建模方法

针对一体化飞行器高度耦合的非线性气动问题,提出了一种基于移动最小二乘法的气动力数据建模方法;首先,对影响模型精度的因素进行了分析;接着,在构建移动最小二乘模型时采用遗传算法获取最佳支撑域半径以及最佳影响因子β,提高近似精度从而达到减少样本点的目的;得到泛化能力较强的气动力模型,并与偏最小二乘方法的建模结果进行对比;实验结果表明:移动最小二乘法的建模效果优于偏最小二乘方法,预测误差较小,证明了将该方法应用于气动数据建模是可行的。     

基于遗传算法的B样条曲线和Bézier曲线的最小二乘拟合

考虑用B样条曲线拟合平面有序数据使得最小二乘拟合误差最小.一般有两种考虑,一种是保持B样条基函数的节点不变,选择参数使得拟合较优.参数的选择方法包括均匀取值、累加弦长法、centripetal model、Gauss-Newton迭代法等.另一种则是先确定好参数值(一般用累加弦长法),然后再用.某一算法计算出节点,使得拟合较优.同时把两者统一考虑,用遗传算法同时求出参数、节点使得拟合在最小二乘误差意义下最优.与Gauss-Newton迭代法、Piegl算法相比,本方法具有较好的鲁棒性(拟合曲线与初始值无关)、较高的精度及控制顶点少等优点.实验结果说明采用遗传算法得到的曲线逼近效果更好.用遗传算法对Bezier曲线拟合平面有序数据也进行了研究.     

The discrete collocation method for Fredholm–Hammerstein integral equations based on moving least squares method

The purpose of this paper is to investigate the discrete collocation method based on moving least squares (MLS) approximation for Fredholm–Hammerstein integral equations. The scheme utilizes the shape functions of the MLS approximation constructed on scattered points as a basis in the discrete collocation method. The proposed method is meshless, since it does not require any background mesh or domain elements. Error analysis of this method is also investigated. Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method.     

基于LSSVM的混沌时间序列的多步预测

结合相空间重构理论和统计学习理论，实现混沌时间序列的多步预测．采用擞熵率法求得最优嵌入维数和时延参数，重构系统相空间，用最小二乘支持向量机建立渑沌时间序列的多步预测模型，并与径向基函数网络预测模型比较．结果表明，所建立的模型能够捕捉到原混沌系统的动力学特征．前者的归一化均方根预测误差远小于径向基函数网络预测模型的预测误差，泛化能力较强．其预测效果较好．     

模糊最小二乘支持向量机回归研究及应用

针对传统支持向量机对训练样本内的噪声和孤立点比较敏感,导致建模精度不高的问题,将模糊集理论引入到最小二乘支持向量机回归中,建立一种基于数据域描述的模糊最小二乘支持向量机回归的数学模型,该方法将样本映射到高维空间,在高维空间中寻找最小包含超球,然后根据样本到超球心的距离确定模糊隶属度的大小,通过仿真实验验证,该算法提高了支持向量机回归的训练精度,将此模型应用于谷氨酸发酵过程菌体浓度预测,结果表明此方法的有效性。     

Topology optimization of compliant mechanisms using element-free Galerkin method

This paper will propose a topology optimization approach for the design of large displacement compliant mechanisms with geometrical non-linearity by using the element-free Galerkin (EFG) method. In this method, the Shepard function is applied to construct a physically meaningful density approximant, to account for its non-negative and range-bounded property. Firstly, in terms of the original nodal density field, the Shepard function method functionally similar to a density filter is used to generate a non-local nodal density field with enriched smoothness over the design domain. The density of any node can be evaluated according to the nodal density variables located inside the influence domain of the interested node. Secondly, in the numerical implementation the Shepard function method is again employed to construct a point-wise density interpolant. Gauss quadrature is used to calculate the integration of background cells numerically, and the artificial densities over all Gauss points can be determined by the surrounding nodal densities within the influence domain of the concerned computational point. Finally, the moving least squares (MLS) method is applied to construct the shape functions using the weight functions with compact support for assembling the meshless approximations of state equations. Since MLS shape functions are lack of the Kronecker delta function property, the penalty method is applied to enforce the essential boundary conditions. A typical large-deformation compliant mechanism is used as the numerical example to demonstrate the effectiveness of the proposed method.     

基于迁移子空间学习的偏最小二乘回归软测量方法

针对流程工业中工况改变易导致当前样本与历史样本分布失配,传统软测量模型失准的问题,考虑工业数据时序性、动态性以及存在过程漂移等特性对建模的影响,提出一种基于迁移子空间学习的偏最小二乘回归软测量方法.首先,回归框架采用非线性迭代偏最小二乘方法,对其求解映射向量的目标函数施加基于子空间重构的域适应正则项,映射过程中保证当前工况中每个样本能够被历史工况样本线性重构.在此基础上对重构矩阵施加低秩稀疏约束,保持数据结构的同时使重构矩阵具备块状结构以应对过程漂移特性.将所提出方法在1个数值案例和3个不同的多工况数据集中进行实验,并与现有域适应回归方法进行对比分析.实验表明,所提出方法能够有效提高模型在跨工况条件下的预测精度,减少工况间数据分布差异对模型性能的影响.     

Implicit regularization of the incomplete oblique projections method

The aim of this paper is to improve the performance of the incomplete oblique projections method (IOP), previously introduced by the authors for solving inconsistent linear systems, when applied to image reconstruction problems. That method employs incomplete oblique projections onto the set of solutions of the augmented system Ax − r = b , and converges to a weighted least squares solution of the system Ax = b . Many tomographic image reconstruction problems are such that the limitation of the range of rays makes the model underdetermined, the discretized linear system is rank-deficient, the nullspace is non-trivial, and the minimal norm least squares solution may be far away from the true image. In a previous paper, we have added a quadratic term reflecting neighboring pixel information to the standard least squares model for improving the quality of the reconstructed images. In this paper we replace the quadratic function by a more general regularizing function avoiding the modification of the original system. The key idea is to perform a joint optimization of the norm of the residual and of the regularizing function in each iteration. The theoretical properties of this new algorithm are analyzed, and numerical experiments are presented comparing its performance with other well-known methods. They show that the new approach improves the quality of the reconstructed images.     

Moving least squares collocation method for Volterra integral equations with proportional delay

In this work, we apply the moving least squares (MLS) method for numerical solution of Volterra integral equations with proportional delay. The scheme utilizes the shape functions of the MLS approximation constructed on scattered points as a basis in the discrete collocation method. The proposed method is meshless, since it does not require any background mesh or domain elements. An error bound is obtained to ensure the convergence and reliability of the method. Numerical results approve the efficiency and applicability of the proposed method.     

基于小波核LS—SVM的网络流量预测

网络流量预测对大规模网络管理、规划、设计具有重要意义。支持向量机方法是近年来发展起来的新型机器学习算法,用于解决高度非线性分类及回归问题。介绍了基于小波核最小二乘支持向量机的网络流量预测方法,利用小波核函数的多分辨特性提高了支持向量机的非线性建模能力。通过对实测网络流量数据的学习,对未来网络流量进行预测。实验结果表明,取得了较好的预测效果。