Algorithms and statistical analysis for linear structured weighted total least squares problem

Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.

THE WEIGHTED KATO SQUARE ROOT PROBLEMOF ELLIPTIC OPERATORS HAVING A BMOANTI-SYMMETRICPART

Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.

Least Squares One-Class Support Tensor Machine

One-class classification problem has become a popular problem in many fields, with a wide range of applications in anomaly detection, fault diagnosis, and face recognition. We investigate the one-class classification problem for second-order tensor data. Traditional vector-based one-class classification methods such as one-class support vector machine (OCSVM) and least squares one-class support vector machine (LSOCSVM) have limitations when tensor is used as input data, so we propose a new tensor one-class classification method, LSOCSTM, which directly uses tensor as input data. On one hand, using tensor as input data not only enables to classify tensor data, but also for vector data, classifying it after high dimensionalizing it into tensor still improves the classification accuracy and overcomes the over-fitting problem. On the other hand, different from one-class support tensor machine (OCSTM), we use squared loss instead of the original loss function so that we solve a series of linear equations instead of quadratic programming problems. Therefore, we use the distance to the hyperplane as a metric for classification, and the proposed method is more accurate and faster compared to existing methods. The experimental results show the high efficiency of the proposed method compared with several state-of-the-art methods.

Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions

Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.

PSR-SQUARES:基于程序空间约简器的SQL逆向合成系统

针对SQUARES程序空间增长过快,导致程序合成效率偏低的问题,在SQUARES的基础上,增加了以深度神经网络为核心的程序空间约简器,将给定的<被查询表,查询结果>示例表示成二维张量,作为深度神经网络的输入,网络的输出是关于目标SQL语句合成规则的相关性标记向量。约简器根据神经网络的输出结果,采用末N位淘汰策略,删除与目标SQL语句相关性弱的合成规则,以减少候选SQL语句的生成和验证,提升系统合成效率。对约简器中深度神经网络的结构设计、训练样本集的生成方法和网络训练过程进行了详细描述。同时将PSR-SQUARES与当前有代表性SQL逆向合成系统进行实验对比,实验结果表明,PSR-SQUARES的综合性能不同程度地优于其他合成系统,平均合成时间由SQUARES的251 s降低至130 s,目标程序合成成功率由80%提升至89%。

Factor-square-full半模

作为factor-square-full模的真推广,引入了factor-square-full半模的概念.设S是半环,M是左S-半模.称M的真subtractive子半模X是d-square,若存在正规满同态f:M→(M/X)2;称M的真subtractive子半模X是quasi-d-square,若存在M的d-square子半模Y使得X≤Y;称M是factor-square-full,若M的任意真subtractive子半模是quasi-d-square.讨论了这些子半模类及factor-square-full半模的性质.

采用改进遗传算法优化LS-SVM逆系统的外转子无铁心无轴承永磁同步发电机解耦控制

为了实现外转子无铁心无轴承永磁同步发电机(outer rotor coreless bearingless permanent magnet synchronous generator,ORC-BPMSG)的精确控制,提出一种基于改进遗传算法(improved genetic algorithm,IGA)优化最小二乘支持向量机(least square support vector machine,LS-SVM)逆系统的解耦控制策略。首先,基于ORC-BPMSG的结构及工作原理,推导其数学模型,并分析其可逆性。其次,建立LS-SVM回归方程,并采用IGA优化LS-SVM的性能参数,从而训练得到逆系统。然后,将逆系统与原系统串接,形成伪线性系统,实现了ORC-BPMSG的线性化和解耦。最后,将提出的控制方法与传统LS-SVM逆系统控制方法进行对比仿真和实验。仿真和实验结果表明:所提出的控制策略可以较好地实现ORC-BPMSG输出电压和悬浮力、以及悬浮力之间的解耦控制。

基于TLS的改进子空间投影算法

针对经典MUSIC算法在信源相干、低信噪比、小快拍数等非理想环境下性能失效的问题,提出了一种改进的基于TLS的加权子空间投影算法。首先对阵列接收的数据协方差矩阵进行重构处理,以达到解相干目的;其次充分利用子空间信息,基于总体最小二乘拟合方法对特征值进行拟合修正,基于修正MUSIC算法思想,利用校正后的噪声特征值和信号特征值分别对噪声子空间和信号子空间进行加权处理,得到改进后的噪声子空间和信号子空间,并将两者结合得到新的空间谱函数;最后进行谱峰搜索,完成信号源的波达方向估计。仿真结果表明,改进后的算法既适用于相干信号环境,在低信噪比、小快拍数及信号入射角度间隔较小的情况下,又能有效估计出信源的波达方向。

硫酮衍生物LS对天然胶乳保存效果的研究

天然胶乳很容易腐败变质,而当前的高氨保存体系存在严重的污染问题。本研究采用硫酮衍生物LS保存天然胶乳,研究保存剂LS对天然胶乳的保存效果。结果表明:LS保存的鲜胶乳挥发脂肪酸值(VFA No.)和黏度值均比较低,当LS用量为0.1%时,对鲜胶乳的保存效果优于0.25%氨;采用LS-氨复合保存制备低氨浓缩胶乳,当LS用量为0.01%~0.05%时可稳定保存浓缩胶乳达180d之久;所保存的低氨浓缩胶乳挥发脂肪酸值(VFANo.)较低,稳定性良好,各项指标均满足当前生产应用需求。此外,LS-氨复合保存低氨浓缩胶乳具有优异的理化性能和成膜性能,硫化胶膜的拉伸强度和撕裂强度普遍优于当前高氨保存浓缩胶乳。通过红外吸收光谱分析,LS-氨复合保存的低氨浓缩胶乳硫化胶膜的结构无明显变化;热分析结果表明,硫化胶膜热稳定性与高氨浓缩胶乳胶膜基本一致。此外,安全性分析结果表明,LS-氨复合保存低氨浓缩胶乳干胶膜不具有潜在毒性影响;同时无皮肤刺激性反应,安全性良好。硫酮衍生物LS对天然胶乳具有优异的保存效果,复合保存制备低氨浓缩胶乳性能良好,可用于多种纯胶制品的生产,同时使用成本低廉,具有广阔的应用前景。

基于DBN和BES-LSSVM的矿用压风机异常状态识别方法

针对矿用压风机这类分布式系统的异常类别复杂、识别精度低等问题,提出了一种基于深度置信网络(DBN)和最小二乘支持向量机(LSSVM)的异常状态识别方法。首先,分析压风机组成系统及其运行机理,确定常见的异常状态类型;其次,采用DBN无监督学习方式充分挖掘监测数据中异常特征并快速提取;然后,利用秃鹰搜索算法(BES)优化LSSVM的超参数,构建最优的BES-LSSVM分类模型;最后,将DBN提取的异常特征作为BES-LSSVM模型的输入,对矿用压风机异常状态进行识别。试验验证与对比分析结果表明,相较于GA,PSO,GWO算法,BES算法的求解精度和收敛速度均有所提高,同时DBN-BES-LSSVM模型在测试集上平均识别精度达到94.65%,较PCA-LSSVM模型、DBN模型和DBN-LSSVM模型的识别精度分别提高了10.53%,5.84%和3.76%,验证了DBN-BES-LSSVM模型在矿用压风机异常特征提取以及特征识别方面的优越性。

基于ISSA-HKLSSVM的浮选精矿品位预测方法

针对浮选过程变量滞后、耦合特征及建模样本数量少所导致精矿品位难以准确预测的问题,提出了一种基于改进麻雀搜索算法(Improved Sparrow Search Algorithm,ISSA)优化混核最小二乘支持向量机(Hybrid Kernel Least Squares Support Vector Machine,HKLSSVM)的浮选过程精矿品位预测方法.首先采集浮选现场载流X荧光品位分析仪数据作为建模变量并进行预处理,建立基于最小二乘支持向量机(Least Squares Support Vector Machine,LSSVM)的预测模型,以此构建新型混合核函数,将输入空间映射至高维特征空间,再引入改进麻雀搜索算法对模型参数进行优化,提出基于ISSA-HKLSSVM方法实现精矿品位预测,最后开发基于LabVIEW的浮选精矿品位预测系统对本文提出方法实际验证.实验结果表明,本文提出方法对于浮选过程小样本建模具有良好拟合能力,相比现有方法提高了预测准确率,可实现精矿品位的准确在线预测,为浮选过程的智能调控提供实时可靠的精矿品位反馈信息.

基于VMD-LILGWO-LSSVM短期风电功率预测

目的为了减小风电功率并入国家电网时产生的频率波动,提高风电功率预测精度,方法提出一种结合变分模态分解(VMD)、改进灰狼算法(LILGWO)和最小二乘支持向量机(LSSVM)的风电功率短期预测方法。首先通过VMD方法将风电功率序列分解重构成3个复杂程度性不同的模态分量,降低风电功率的波动性;其次使用LSSVM挖掘各分量的特征信息,对各分量分别进行预测,针对LSSVM模型中重要参数的选取对预测精度影响较大问题,引入LILGWO对参数进行寻优;最后将各分量预测结果叠加重构,得到最终预测风电功率。结果以宁夏回族自治区某地区风电站实际数据为例,对未来三天分别进行预测取平均值,本文方法的预测平均绝对误差(mean absolute error,MAE)为2.7068 kW,均方根误差(root mean square error,RMSE)为2.0211,拟合程度决定系数(R-Square,R^(2))为0.9769,与对比方法3~6相比,RMSE分别降低了40.93%,25.21%,14.7%,6.24%;MAE分别降低了42.34%,28.04%,16.97%,7.77%;R^(2)分别提升了4.21%,1.78%,0.82%,0.28%。预测时长方面,BP和LSSVM平均训练时间分别是10,138 s,虽然LSSVM预测时间较长但效果最好,采用PSO、GWO、LILGWO对LSSVM进行寻优后训练时间分别平均缩短了39,44,58 s。结论仿真验证了所提方法在短期风电功率预测方面的有效性。

基于分数阶LS模型的多场耦合波的反射和透射

应用麦克斯韦电磁学理论引入洛伦兹力,反映外磁场对弹性波传播的影响,运用分数阶广义热弹性LS模型,反映热力耦合效应对弹性波传播的影响.通过色散方程,分析了外磁场和热力耦合效应对波动模式和色散特性的影响.应用连续性边界条件计算出各种反射波和透射波与入射波的能流比,并通过法向能量守恒验证了数值计算结果的可靠性.

Electrochemical Machining Analysis on Grid Cathode Composed of Square Cells

During the electrochemical machining (ECM), the cathodes designed by the existing methods are mainly unitary cathodes, which can be only used to produce the workpieces with the same shapes. However, there are few researches on designing cathodes for machining the different workpieces with the different surfaces. This paper presents the grid cathode composed of the square cells to produce the workpieces with different shapes. Three types of the square cells, 2.5 mm′2.5 mm, 3 mm′3 mm, and 4 mm′4 mm, are utilized to construct the plane, the slant, and the blade cathode. The material of the cathode and the anode is CrNi 18 Ti 9 , and the ingredient of electrolyte is 15% NaCl and 15% NaNO 3 . The machining equilibrium machining current and time are acquired and analyzed, the machining process and the workpiece quality are compared between using the grid cathode and the unitary cathode. Moreover, the machining errors on the workpiece surface are measured and analyzed, and the error reasons are traced and discussed to obtain the better surface quality of the workpiece. The experiment and analysis results show that the grid cathode can be used to manufacture the workpieces with complex shapes in certain range of the error. The workpiece quality improves with the size of the square cell being reduced, and if the square element is small enough, the workpiece quality is almost equal to the one machined by the unitary cathode. The proposed research realizes a single cathode machining the different workpieces with the different surfaces.

Application of Least Square Support Vector Machine (LSSVM) for Determination of Evaporation Losses in Reservoirs

This article adopts Least Square Support Vector Machine (LSSVM) for prediction of Evaporation Losses (EL) in reservoirs. LSSVM is firmly based on the theory of statistical learning, uses regression technique. The input of LSSVM model is Mean air temperature (T) (?C), Average wind speed (WS)(m/sec), Sunshine hours (SH)(hrs/day), and Mean relative humidity(RH)(%). LSSVM has been used to compute error barn of predicted data. An equation has been developed for the determination of EL. Sensitivity analysis has been also performed to investigate the importance of each of the input parameters. A comparative study has been presented between LSSVM and artificial neural network (ANN) models. This study shows that LSSVM is a powerful tool for determination EL in reservoirs.

Mechanical properties of wood materials using near-infrared spectroscopy based on correlation local embedding and partial least-squares

This study used near-infrared(NIR)spectroscopy to predict mechanical properties of wood.NIR spectra were collected in wavelengths 900–1700 nm,and spectra averaged by radial and tangential surface spectra were used to establish a partial least square(PLS)model based on correlation local embedding(CLE).Mongolian oak(Quercus mongolica Fisch.ex Ledeb.)was used to test the eff ectiveness of the model.The cross-validation method was used to verify the robustness of the CLE–PLS model.Ninety samples were tested as the calibration set and forty-fi ve as the validation set.The results show that the prediction coeffi cient of determination(R2 p)is 0.80 for MOR,and 0.78 for MOE.The ratio of performance to deviation is 2.23 for MOR and 2.15 for MOE.

Deposition of cerium contained conversion films on LC4 alloy with square wave pulse method

Cerium contained conversion films were deposited on LC4 aluminum alloy usingsquare wave pulse (SWP) in a CeCl_3 solution with KMnO_4 as the oxidant. Energy dispersivespectroscopy (EDS) and scanning electron microscopy (SEM) were adopted to study the composition andthe morphology of the film. It is found that the film is composed of Al, Zn, Cu, and small amount ofcerium. The polarization curves of the specimens treated with SWP technique measured in 3.5% (massfraction) NaCl solution reveal that the film thus formed inhibits both the anodic and cathodicprocess of the corrosion of the specimen. The immersion tests of treated specimens in 3.5% NaClsolution indicate that the corrosion resistance of the SWP treated specimen is better than that ofthe untreated and is equivalent to or even better than that of the traditionally electro-chemicallytreated specimens.

Revisiting Akaike’s Final Prediction Error and the Generalized Cross Validation Criteria in Regression from the Same Perspective: From Least Squares to Ridge Regression and Smoothing Splines

In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.

A novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise,minimum mean square variance criterion and least mean square adaptive filter

Underwater acoustic signal processing is one of the research hotspots in underwater acoustics.Noise reduction of underwater acoustic signals is the key to underwater acoustic signal processing.Owing to the complexity of marine environment and the particularity of underwater acoustic channel,noise reduction of underwater acoustic signals has always been a difficult challenge in the field of underwater acoustic signal processing.In order to solve the dilemma,we proposed a novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise(CEEMDAN),minimum mean square variance criterion(MMSVC) and least mean square adaptive filter(LMSAF).This noise reduction technique,named CEEMDAN-MMSVC-LMSAF,has three main advantages:(i) as an improved algorithm of empirical mode decomposition(EMD) and ensemble EMD(EEMD),CEEMDAN can better suppress mode mixing,and can avoid selecting the number of decomposition in variational mode decomposition(VMD);(ii) MMSVC can identify noisy intrinsic mode function(IMF),and can avoid selecting thresholds of different permutation entropies;(iii) for noise reduction of noisy IMFs,LMSAF overcomes the selection of deco mposition number and basis function for wavelet noise reduction.Firstly,CEEMDAN decomposes the original signal into IMFs,which can be divided into noisy IMFs and real IMFs.Then,MMSVC and LMSAF are used to detect identify noisy IMFs and remove noise components from noisy IMFs.Finally,both denoised noisy IMFs and real IMFs are reconstructed and the final denoised signal is obtained.Compared with other noise reduction techniques,the validity of CEEMDAN-MMSVC-LMSAF can be proved by the analysis of simulation signals and real underwater acoustic signals,which has the better noise reduction effect and has practical application value.CEEMDAN-MMSVC-LMSAF also provides a reliable basis for the detection,feature extraction,classification and recognition of underwater acoustic signals.

Experimental Study of Submergence Ratio on Local Scour Around a Square Pile in Steady Flow

Scour around a submerged square pile was realized experimentally in a steady flow to study the effects of flow depth on local scour.Flow depth to pile height ratios ranging from 1.5 to 5 in uniform sand and 2 to 5 in non-uniform sand were tested in the approaching flow velocity to critical velocity(larger than which the sediment particle is motivated)ratios of 0.56 and 1.03,respectively.The influences of flow depth were investigated on the basis of analysis of the three-dimensional topography,temporal maximum scour depth,bed profile development,and equilibrium scour depth.Results showed that the maximum scour depth was at the upstream corners of the pile other than at the stagnation point.The evolutions of the maximum scour depth data in non-uniform sand were well fitted with a recent exponential function,which characterized the initial,developing,and equilibrium stages of scour depth.The scour hole slopes upstream of the pile were found to be parallel to each other in the process of each test and were mainly governed by the sediment repose underwater.The equilibrium scour depth varied slightly with flow depth when the submergence ratio was larger than 1 in uniform sand while it was 2 in non-uniform sand.The armoring effects of coarse sediment particles markedly reduced the sediment transport in non-uniform sand despite the 0.34 increment in non-uniformity.